Solve Equations With Variables on Both Sides Section 1.5 Advanced Algebra 1.

Solve Equations With Variables on Both Sides

Section 1.5

Advanced Algebra 1

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Steps to Solve Equations with Variables on Both Sides

1) Simplify each side Get rid of double Negatives

Get rid of fractions Distribute Combine Like Terms 2) Move variables to same side “Smaller to the bigger” 3) Solve by using INVERSE Operations

Use Steps to Solve Equation:

-3x + 4 = 5x – 8+3x +3x

Get variables on same side of equation – use inverse operation (add 3x)

4 = 8x - 8Solve 2 step equation + 8 +8

12 = 8x 8 8

x = 3/2

Use Steps to Solve Equation:2(x + 7) + 3 = 5x - 1

2x + 14 + 3 = 5x – 1 distribute

Combine like terms 2x + 17 = 5x - 1 -2x -2x Get variables on same side –

use inverse operation17 = 3x - 1Solve 2 step equation +1 +1

18 = 3x 3 3

x = 6

Use Steps to Solve Equation:4(1 – 2x) = 4 – 6x

4 – 8x = 4 - 6x Get rid of ( ) -- distribute

Get variables on same side – use inverse operation (add 8x) 4 = 4 + 2xSolve 2 step equation - 4 - 4

0 = 2x 2 2

x = 0

+8x + 8x

Use Steps to Solve Equation:

9 + 5x = 5x + 9 -5x -5x

Get variables on same side of equation – use inverse operation (subtract 5x)

When solving, if you get a TRUE STATEMENT, then that means that any real number works.

9 = 9

Infinite Solutions

Use Steps to Solve Equation:

6x – 1 = 6x – 8-6x -6x

Get variables on same side of equation – use inverse operation (subtract 6x)

The variables zeroed out and remaining is a false statement where a number is equal to a different number, so there will be no number that will work in the equation.

-1 = - 8

x = no solutions

The solution is no real numbers or empty set

3 - 2x = 4x – 6

+ 2x +2x

3 = 6x – 6

+ 6 + 6

9 = 6x

6 6

or 1.5 = x

5) Solve1. Clear the fraction – multiply

each term by the LCD2. Simplify3. Add 2x to both sides4. Simplify5. Add 6 to both sides6. Simplify7. Divide both sides by 68. Simplify9. Check your answer

1.53 1 1 3

8 4 2 41.5

3

2

0.5 + 0.3y = 0.7y – 0.3

1: Move variable to one side0.5 + 0.3y = 0.7y – 0.3

–0.3y –0.3y

0.5 = 0.4y – 0.3

0.8 = 0.4y

+0.3 + 0.3

2 = y

2: add/subtract

3: Multiple/divide

Solve the equation. Check your answer.

Simplifying Each Side BeforeSolving Equations

C: Combine like terms

D: Distributive P.

4 – 6a + 4a = –1 –5(7 – 2a)

4 – 6a + 4a = –1 –5(7) –5(–2a)

4 – 6a + 4a = –1 – 35 + 10a

4 – 2a = –36 + 10a

+2a +2a

4 = -36 + 12a

M: move variable to One side

4 – 6a + 4a = –1 – 5(7 – 2a)

M: multiply/divide

4 = -36 + 12a+ 36 +36

40 = 12a

A: add/subtract

A: Add/subtract

D: Distributive Property

+ 1 + 1

3 = b – 1

M: Move variable to one side

Solve the equation. Check your answer.

4 = b

1. 2m – 6 + 4m = 12

ANSWER 6

Solve the equation.

2. 6a – 5(a – 1) = 11

ANSWER 3

3. A charter bus company charges $11.25 per ticketplus a handling charge of $.50 per ticket, and a $15fee for booking the bus. If a group pays $297 to charter a bus, how many tickets did they buy?

ANSWER 24 tickets

Create an equation, then solve the equation.

ANSWER 2

2. 3b + 2(b – 4) = 47

11ANSWER

3. –6 + 4(2c + 1) = –34

–4ANSWER

1. 8g – 2 + g = 16

Solve the equation.

5. Joe drove 405 miles in 7 hours. He drove at a rate of 55 miles per hour during the first part of the trip and 60 miles per hour during the second part. How many hours did he drive at a rate of 55 miles per hour?

24ANSWER

4. (x – 6) = 1223

3 hANSWER