# Solving equations with variables on both sides When

Solving equations with variables on both sides. When you have variables on both sides, ‘combine’ them by moving them to one side using inverse operations (opposites). Usually we move the variable to the left side, but if it makes the variable negative, you might want to move it to the right side to keep it positive. Your answer must have a variable positive! Either way you will get the same answer.

Solve both ways: 9 x – 8 = 4 x + 12 -4 x 5 x – 8 = 12 +8 + 8 5 x = 20 5 5 x=4 9 x – 8 = 4 x + 12 -9 x – 8 = -5 x + 12 -20 = -5 x -5 -5 4=x

(15 x – 24) = 8 + 4(x-3) 5 x - 8 = 8 + 4 x - 12 5 x - 8 = - 4 + 4 x -4 x x-8=-4 +8 +8 x=4

When will I ever use this? ? ? You want to rent video games and can’t decide which store to rent from. Store 1 charges $8 per game for 3 days and no membership fee. Store 2 charges a $50 membership fee, plus $3 per game for 3 days. Which store is a better choice?

Set up an equation to solve. Hint: set both stores equal to each other. This will give you the break even point. Write a verbal model. Label the unknown. Write the equation. Solve Answer the question.

Solution: Store 1 rental fee #rentals=Store 2 membership fee+rental fee #rentals. Let x = number of games rented. 8 x=50+3 x 5 x=50 x=10 After 10 rentals Store 2 would be a better choice.

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