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### Solving Equations with Variables on Both Sides

• To solve equations with variables on both sides, bring all the variable terms to one side of the equation. Use the Distributive Property, if necessary, collect like terms, and simplify.
• To solve equations with variables on both sides, simplify as much as you can on both sides before you apply inverse operations to isolate the variable.

## 5x + 15 = 8x. Solve for x.

• 5x − 8x = − 15
• − 3x = − 15

## − 8 − 4x = 10 + 3x. Solve for x.

• − 8 − 10 = 3x + 7x
• − 18 = 10x
• x = − [18/10]

## 4x + 5 = 3(2x + 1). Solve for x.

• 4x + 5 = 6x + 3
• 4x − 6x = 3 − 5
• − 2x = − 2

## 11 − 5x + 3 = − 3x − 10. Solve for x.

• − 5x + 3x = − 10 − 11 − 3
• − 2x = − 24

## 3.6x = 4(x − 2). Solve for x.

• 3.6x = 4x − 8
• 3.6x − 4x = − 84
• − 0.4x = − 8

## 35 + 7x = 24 + x + 1. Solve for x.

• 7x − x = 24 + 1 − 35
• 6x = 25 − 35
• 6x = − 104

## 14.5 + 5x = − 3.3x − 10.4. Solve for x.

• 5x + 3.3x = − 10.4 − 14.5
• 8.3x = − 24.9

## − 3(5x − 2) = − 18x + 10x. Solve for x.

• − 15x + 6 = − 8x
• − 15x + 8x = − 6
• − 7x = − 6

## Two boats are taking the same path to a destination. Ship A travels at 25 mi/hr, while ship B travels at 30 mi/hr and leaves 30 min after ship A does. How long after ship A leaves will ship B catch up to ship A?

• Let t = time that ship A travels before ship B catches up.
• distanceship A = distanceship B
distance = rate × time
• 25 mi/hr ×t = 30 mi/hr × (t - 0.5)
• 25t = 30t − 15
• 25t − 30t = − 15
• − 5t = − 15

## Lisa runs [1/8] mi/min. George runs [1/10] mi/min. Lisa starts running 5 min after George starts. How long after George starts running have they run the same distance?

• Let t = number of minutes
• distanceLisa = distanceGeorge
distance = rate × time
• [1/8](t − 5) = [1/10]t
• [1/8]t − [5/8] = [1/10]t
• [1/8]t − [1/10]t = [5/8]
• [5/40]t − [4/40]t = [25/40]
• [1/40]t = [25/40]

### t = 25 min

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.