Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

Solving Equations with

Variables on Both Sides

Pre-Algebra

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

To solve multistep equations with variables on both sides:

1.First combine like terms.

2.Then add or subtract variable terms to both sides so that the variable occurs on only one side of the equation.

3.Then use properties of equality to isolate the variable.

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

Solve.

A. 4x + 6 = x

Example 1:

4x + 6 = x– 4x – 4x

6 = –3x

Subtract 4x from both sides.

Divide both sides by –3.

–2 = x

6–3

–3x–3=

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

Solve.

B. 9b – 6 = 5b + 18

Example 2:

9b – 6 = 5b + 18– 5b – 5b

4b – 6 = 18

4b 4

24 4 =

Subtract 5b from both sides.

Divide both sides by 4.

b = 6

+ 6 + 6

4b = 24Add 6 to both sides.

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

Solve.

C. 9w + 3 = 5w + 7 + 2w

Example 3:

9w + 3 = 5w + 7 + 2w

2w + 3 = 7

9w + 3 = 7w + 7 Combine like terms.

– 7w – 7w Subtract 7w from both sides.

2w = 4

– 3 – 3 Subtract 3 from both sides.

Divide by 2 on both sides.

w = 2

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

Solve.

A. 10z – 15 – 4z = 8 – 2z - 15

Example 4:

10z – 15 – 4z = 8 – 2z – 15

+ 15 +15

6z – 15 = –2z – 7 Combine like terms.+ 2z + 2z Add 2z to both sides.

8z – 15 = – 7

8z = 8

z = 1

Add 15 to both sides.

Divide both sides by 8.8z 88 8=

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

Xavier & Jonathon have the same number of super hero action figures in their collections. Xavier has 5 complete sets and 4 individual figures. Jonathon has 3 complete sets and 14 individual figures. How many figures make up a complete set?

Let x equal the number of figures in a complete set.5x + 4 = 3x + 14

Now solve…

Pre-Algebra

10-3 Solving Equations with Variables on Both Sides

5x + 4 = 3x + 14

– 3x – 3x

2x + 4 = 14

Subtract 3x from both sides.

– 4 – 4 Subtract 4 from both sides.

2x = 10

2x2

102= Divide both sides by 2.

x = 5 Each complete set has 5 super hero action figures.