Solving for X

Solving for XSolving for X

This presentation will guide This presentation will guide you through solving a one-you through solving a one-step or two-step equation.step or two-step equation.

The buttons below will help you move through this The buttons below will help you move through this lesson. At any time, use the “left arrow” button to go lesson. At any time, use the “left arrow” button to go back to the previous slide or the “right arrow” to go to back to the previous slide or the “right arrow” to go to

the next slide. Use the “home” button to come back to the next slide. Use the “home” button to come back to the beginning page. the beginning page.

“Left Arrow” “Home” “Right Arrow”

Solving for XSolving for XFirst First choosechoose your starting level. your starting level.

1.1.One step equationsOne step equations2.2.Two step equationsTwo step equations

Solving for XSolving for XHow to solve a one – step equationHow to solve a one – step equation

Object: To solve an equation, you must get Object: To solve an equation, you must get the variable by itself to determine it’s the variable by itself to determine it’s value.value.

To solve for x, you must “undo” the four To solve for x, you must “undo” the four operations that we use in everyday operations that we use in everyday mathematics. Those operations include mathematics. Those operations include addition, subtraction, multiplication, and addition, subtraction, multiplication, and division.division.

We must also keep the equation balanced. We must also keep the equation balanced. What we do to one side of the equation, What we do to one side of the equation, we have to do to the other side of the we have to do to the other side of the equation. More specifically, the operation equation. More specifically, the operation that we perform on the left side of the that we perform on the left side of the equation we have to perform on the right equation we have to perform on the right side of the equation.side of the equation.

An example of addition in an equation isAn example of addition in an equation is

X + 4 = 243.X + 4 = 243. Here we are adding 4 to an unknown Here we are adding 4 to an unknown

value and it equals 243. To undo addition, value and it equals 243. To undo addition, we must use subtraction. we must use subtraction.

X + 4 X + 4 – 4– 4 = 243 = 243 – 4– 4 In this example, x is equal to 239.In this example, x is equal to 239.

An example of subtraction in an equation An example of subtraction in an equation isis

X – 6 = 33.X – 6 = 33. Here we are subtracting 6 from an Here we are subtracting 6 from an

unknown value and it equals 33. To undo unknown value and it equals 33. To undo subtraction, we must use addition. subtraction, we must use addition.

X – 6 X – 6 + 6+ 6 = 33 = 33 + 6+ 6 In this example, x is equal to 39.In this example, x is equal to 39.

An example of multiplication in an An example of multiplication in an equation isequation is

3X = 6.3X = 6. Here we are multiplying 3 by an unknown Here we are multiplying 3 by an unknown

value and it equals 6. To undo value and it equals 6. To undo multiplication, we must use division. multiplication, we must use division.

3X 3X / 3/ 3 = 6 = 6 / 3/ 3 In this example, x is equal to 2.In this example, x is equal to 2.

An example of division in an equation is An example of division in an equation is

X / 4 = 12.X / 4 = 12.

Here we are dividing an unknown value by Here we are dividing an unknown value by 4 and it equals 12. To undo division, we 4 and it equals 12. To undo division, we must use multiplication.must use multiplication.

X / 4 X / 4 * 4* 4 = 12 = 12 * 4* 4

In this example, x is equal to 48.In this example, x is equal to 48.

Let’s try a few examples!Let’s try a few examples!

X + 16 = 24X + 16 = 24In this example, to solve for X we need to:In this example, to solve for X we need to:

A. Add 16 to both sides.A. Add 16 to both sides.

B. Subtract 16 from both sides.B. Subtract 16 from both sides.

C. Multiply both sides by 16.C. Multiply both sides by 16.

D. Divide both sides by 16.D. Divide both sides by 16.

Not quite! Here’s why:Not quite! Here’s why:

X + 16 = 24X + 16 = 24To “undo” addition, we must subtract 16 To “undo” addition, we must subtract 16 from both sides of the equation like this:from both sides of the equation like this:

X + 16 X + 16 – 16 – 16 = 24 = 24 –16–16

Click here to go back to the quiz.

Way to go!Way to go!

You’re right! To “undo” addition, we must You’re right! To “undo” addition, we must subtract from both sides of the equation.subtract from both sides of the equation.

X + 16 X + 16 – 16 – 16 = 24 = 24 – 16– 16

Try another one!Try another one!

X – 12 = 36X – 12 = 36In this example, to solve for X we need to:In this example, to solve for X we need to:






X – 12 = 36X – 12 = 36To “undo” addition, we must subtract 12 To “undo” addition, we must subtract 12 from both sides of the equation like this:from both sides of the equation like this:

X – 12 X – 12 + 12 + 12 = 36 = 36 + 12+ 12



You’re right! To “undo” addition, we must You’re right! To “undo” addition, we must add to both sides of the equation.add to both sides of the equation.

X – 12 X – 12 + 12 + 12 = 36 = 36 + 12+ 12


4X = 324X = 32In this example, to solve for X we need to:In this example, to solve for X we need to:






4X = 324X = 32To “undo” multiplication, we must divide To “undo” multiplication, we must divide both sides of the equation by 4 like this:both sides of the equation by 4 like this:

4X 4X / 4/ 4 = 32 = 32 / 4/ 4



You’re right! To “undo” multiplication, we You’re right! To “undo” multiplication, we must divide both sides of the equation by must divide both sides of the equation by 4.4.

4X 4X / 4/ 4 = 32 = 32 / 4/ 4


X / 5 = 7X / 5 = 7In this example, to solve for X we need to:In this example, to solve for X we need to:






X / 5 = 7X / 5 = 7To “undo” division, we must multiply both To “undo” division, we must multiply both sides of the equation by 5 like this:sides of the equation by 5 like this:

X / 5 X / 5 * 5 * 5 = 7 = 7 * 5* 5



You’re right! To “undo” division, we must You’re right! To “undo” division, we must multiply both sides of the equation by 5.multiply both sides of the equation by 5.

X / 5 X / 5 * 5 * 5 = 7 = 7 * 5* 5

You’ve done great! Now it’s time to try two-step equations. You’ve done great! Now it’s time to try two-step equations. To go on, click on the right arrow. To go back to the To go on, click on the right arrow. To go back to the

beginning, click on the home button.beginning, click on the home button.

Solving for XSolving for XHow to solve a two – step equationHow to solve a two – step equation

Object: To solve a two-step equation, you Object: To solve a two-step equation, you must get the variable by itself to determine must get the variable by itself to determine it’s value. However, getting the variable by it’s value. However, getting the variable by itself requires one more step than the itself requires one more step than the previous equations.previous equations.

First, you must move any number that First, you must move any number that does not have a variable to the other side does not have a variable to the other side of the equal sign. You do this by “undoing” of the equal sign. You do this by “undoing” addition or subtraction.addition or subtraction.

Second, you follow the directions that we Second, you follow the directions that we learned before to get the variable by itself.learned before to get the variable by itself.

An example of a two step equation isAn example of a two step equation is

3X + 5 = 17.3X + 5 = 17.

Here we are adding 5 to some number multiplied Here we are adding 5 to some number multiplied by three and it equals 17. Our first step is to by three and it equals 17. Our first step is to undo addition by subtracting 5 on both sides of undo addition by subtracting 5 on both sides of the equation.the equation.

3X + 5 3X + 5 – 5 – 5 = 17 = 17 – 5 – 5

This simplifies to 3X = 12. Next we need to This simplifies to 3X = 12. Next we need to undo multiplication by dividing both sides by 3.undo multiplication by dividing both sides by 3.

3X 3X / 3 / 3 = 12 = 12 / 3 / 3

In this example x is equal to 4.In this example x is equal to 4.

Another example of a two step equation isAnother example of a two step equation is

5X – 4 = 26.5X – 4 = 26.

Here we are subtracting 4 from some number Here we are subtracting 4 from some number multiplied by five and it equals 26. Our first step multiplied by five and it equals 26. Our first step is to undo subtraction by adding 4 to both sides is to undo subtraction by adding 4 to both sides of the equation.of the equation.

5X – 4 5X – 4 + 4 + 4 = 26 = 26 + 4 + 4

This simplifies to 5X = 30. Next we need to This simplifies to 5X = 30. Next we need to undo multiplication by dividing both sides by 5.undo multiplication by dividing both sides by 5.

5X 5X / 5 / 5 = 30 = 30 / 5 / 5

In this example x is equal to 6.In this example x is equal to 6.

Let’s try a few examples!Let’s try a few examples!

4X + 16 = 644X + 16 = 64In this example, the first step to solve for X In this example, the first step to solve for X

is:is:






4X + 16 = 644X + 16 = 64First, you must move any number that First, you must move any number that does not have a variable to the other side does not have a variable to the other side of the equal sign. You do this by of the equal sign. You do this by subtracting 16 from both sides of the subtracting 16 from both sides of the equation like this:equation like this:

4X + 16 4X + 16 – 16 – 16 = 64= 64 – 16 – 16 Click here to go back to the quiz.


You’re right! First, you must move any You’re right! First, you must move any number that does not have a variable to number that does not have a variable to the other side of the equal sign. You do the other side of the equal sign. You do this by subtracting 16 from both sides of this by subtracting 16 from both sides of the equation like this:the equation like this:

4X + 16 4X + 16 – 16 – 16 = 64= 64 – 16 – 16

Let’s work on the second step..Let’s work on the second step..

4X + 16 4X + 16 – 16 – 16 = 64= 64 – 16 – 16 In this example, the second step to solve for In this example, the second step to solve for

X is:X is:A. Add 16 to both sides.A. Add 16 to both sides.B. Subtract 16 from both sides.B. Subtract 16 from both sides.C. Multiply both sides by 4.C. Multiply both sides by 4.D. Divide both sides by 4.D. Divide both sides by 4.


4X + 16 4X + 16 – 16 – 16 = 64= 64 – 16 – 16This simplifies to 4x = 48. Next we need to This simplifies to 4x = 48. Next we need to undo multiplication by dividing both sides undo multiplication by dividing both sides by 4.by 4.

4X 4X / 4 / 4 = 48 = 48 / 4/ 4



You’re right!You’re right! Next we need to undo Next we need to undo multiplication by dividing both sides by 4.multiplication by dividing both sides by 4.

4X 4X / 4 / 4 = 48 = 48 / 4/ 4In this example, x is equal to 12.In this example, x is equal to 12.


6X – 8 = 586X – 8 = 58In this example, the first step to solve for X In this example, the first step to solve for X

is:is:A. Add 8 to both sides.A. Add 8 to both sides.B. Subtract 8 from both sides.B. Subtract 8 from both sides.C. Multiply both sides by 6.C. Multiply both sides by 6.D. Divide both sides by 6.D. Divide both sides by 6.


6X – 8 = 586X – 8 = 58First, you must move any number that First, you must move any number that does not have a variable to the other side does not have a variable to the other side of the equal sign. You do this by adding 8 of the equal sign. You do this by adding 8 to both sides of the equation like this:to both sides of the equation like this:

6X – 8 6X – 8 + 8 + 8 = 58= 58 + 8 + 8

Click here to go back to the quiz


You’re right! First, you must move any You’re right! First, you must move any number that does not have a variable to number that does not have a variable to the other side of the equal sign. You do the other side of the equal sign. You do this by adding 8 to both sides of the this by adding 8 to both sides of the equation like this:equation like this:

6X – 8 6X – 8 + 8 + 8 = 58= 58 + 8 + 8

Let’s work on the second step..Let’s work on the second step..

6X – 8 6X – 8 + 8 + 8 = 58= 58 + 8 + 8In this example, the second step to solve for In this example, the second step to solve for

X is:X is:A. Add 8 to both sides.A. Add 8 to both sides.B. Subtract 8 from both sides.B. Subtract 8 from both sides.C. Multiply both sides by 6.C. Multiply both sides by 6.D. Divide both sides by 6.D. Divide both sides by 6.


6X – 8 6X – 8 + 8 + 8 = 58= 58 + 8 + 8This simplifies to 6x = 66. Next we need to This simplifies to 6x = 66. Next we need to undo multiplication by dividing both sides undo multiplication by dividing both sides by 6.by 6.

6X 6X / 6 / 6 = 66 = 66 / 6/ 6



You’re right!You’re right! Next we need to undo Next we need to undo multiplication by dividing both sides by 6.multiplication by dividing both sides by 6.

6X 6X / 6 / 6 = 66 = 66 / 6/ 6In this example, x is equal to 11.In this example, x is equal to 11.

Solving for X

Documents