Solving Two-Step Solving Two-Step Equations Equations You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations? TP: Construct and solve two step equations for real world problems by combining like terms
Solving Two-Step Equations You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations?
Dec 21, 2015
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Solving Two-StepSolving Two-StepEquationsEquations
You will solve equations by undoing operations using properties of equality.
Essential Question: How do you solve two-step equations?
TP: Construct and solve two step equations for real world problems by combining like
terms
Whatever you do to one side, you must Whatever you do to one side, you must do to the other side to keep property do to the other side to keep property of equality.of equality.
Steps for Solving Two-Step Equations
1.Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation.
2.Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.
Inverse Operations Addition SubtractionMultiplication Division
Example 1: Solve 4x – 5 = 15
4x – 5 = 15 +5 +5 (Add 5 to both sides)4x = 20(Simplify) 4 4 (Divide both sides by 4)x = 5 (Simplify)Check:
4(5) -5 =15 20 – 5 = 15 15 =15
EXAMPLE 2 Solve a two-step equation
Solve + 5 = 11.x2
Write original equation.+ 5 = x2
11
+ 5 – 5 = x2 11 – 5 Subtraction Property of Equality
= x2
6 Simplify.
2 =x2 2 6 Multiplication Property of Equality.
x = 12 Simplify.
ANSWER
The solution is 12. Check by substituting 12 for x in the original equation.
EXAMPLE 2 Solve a two-step equation
CHECK + 5 = x2
11 Write original equation.
11+ 5 = 122
?Substitute 12 for x.
Simplify. Solution checks.11 = 11
GUIDED PRACTICE for Example 1 &2
Solve the equation. Check your solution.
1. 5x + 9 = 24
SOLUTION
5x + 9 = 24 Write original equation.
5x + 9 – 9 = 24 – 9 Subtraction Property of Equality
5x = 15 Simplify.
5x5 = 15
5Division Property of Equality
x = 3 Simplify.
GUIDED PRACTICE for Example 1
CHECK
Simplify. Solution check.
Substitute 3 for x.
ANSWER
The solution is 3. Check by substituting 3 for x in the original equation.
5x + 9 = 24 Write original equation.
245 3 + 9 =?
24 = 24
GUIDED PRACTICE for Example 1
Solve the equation. Check your solution.
2. 4y – 4 = 16
SOLUTION
4y – 4 = 16 Write original equation.
4y – 4 + 4 = 16 + 4 Addition Property of Equality
4y = 20 Simplify.
4y4
20
4= Division Property of Equality.
y = 5 Simplify.
GUIDED PRACTICE for Example 1
ANSWER
The solution is 5. Check by substituting 5 for y in the original equation.
CHECK
Simplify. Solution checks.
Substitute 5 for y.
4y – 4 = 16 Write original equation.
164(5) – 4 =?
16 = 16
GUIDED PRACTICE for Example 1
Solve the equation. Check your solution.
SOLUTION
Write original equation.
Add 7 to each side.
Simplify.
Multiply each side by 3.
Simplify.
3. – 1 = –7z3
– 1 = z3 – 7
– 1 + 7 = z3 – 7 + 7
6 = z3
6 =3 z33
18 = z
GUIDED PRACTICE for Example 1
ANSWER
The solution is 18. Check by substituting 18 for z in the original equation.
CHECK
Simplify. Solution checks.
Substitute 18 for z.
Write original equation.– 1 = z3 – 7
183 – 7– 1 =
?
– 1 = – 1
Solve a two-step equation by combining like terms
EXAMPLE 3
Solve 7x – 4x = 21
7x – 4x = 21 Write original equation.
3x = 21 Combine like terms.
Divide each side by 3.
x = 7 Simplify.
= 33x
321
GUIDED PRACTICE for Examples 3
8t – 3t = 35 Write original equation.
5t = 35 Substract the like terms
Divide each side by 5
t = 7 Simplify.
5 =5t 535
5. 8t – 3t = 35
Solve the equation. Check your solution.
GUIDED PRACTICE for Examples 3
CHECK 8t – 3t = 35 Write original equation.
Multiply.
35 =35
8(7) – 3(7) = 35? Substitute 7 for t.
56 – 21 = 35?
Simplify. Solution checks.
GUIDED PRACTICE for Example 4
10. Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work?
Jobs
Write the equation
53–13 = 13 –13 + 8h
53 = 13 + 8h
40 = 8h Simplify.
Subtraction Property of Equality.
SOLUTION
5 = h Division Property of Equality
GUIDED PRACTICE for Example 4
ANSWER
She worked for 5 hours
Essential Question: Essential Question:
How do you solve two-step equations?
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