Equations with the Variable on Both Sides

Warm Up

1. b + 4 = 2b – 5 4. 10h + 12 = 8h + 4

2. -6x – 29 = 5x – 7 5. 7a – 17 = 4a + 1

3. -n + 5 = n – 11 6. 5p + 8 = 7p + 2

A square and an equilateral triangle have the same perimeter. The length of each of side of the

square, in feet, is x + 8. The length of each side of the equilateral triangle, in feet, is 4x. Find the

length of each side of the square and the triangle and the perimeter

of each figure.

Peppy Pets charges a flat fee of$15 plus $3 per hour to keep a dog

during the day. Happy Hounds charges

a flat fee of $21 plus $1 per hour. For

how many hours is the total feecharged by the companies the

same?

You can represent and solve equations with the variable on both sides by using

algebra tiles to model and solve equations with the variable on both

sides. You can also use inverse operations to get the variable terms on

one side of the equal sign and the constant terms on the other side, and

then divide both sides by the coefficient of the resulting variable term.

A handyman charges an initial fee of $150 and $25 per hour to paint.

Why couldn’t this situation be modeled by the expression

150 - 25x ?

What is the method for solving an equation with the same variable on both sides of the

equation?

Add or subtract the same terms, for example 3x or 7, on both sides of the equation to get the variable term on one side of the equation and

the constant term on the other side of the equation. Then solve the resulting equation by

dividing both sides by the coefficient of the variable.

At Silver Gym, membership is $25 per month, and personal training

sessions are $30 each. At Fit Factor, membership is $65 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would

Sarah have to buy to make the total cost at the two gyms equal?

You can solve an equation with the variable on both sides by using inverse operations to get the

variable terms on one side of the equal sign and the constant terms

on the other side, and then dividing both sides by the

coefficient of the resulting variable term.

Exit Ticket1. 3x + 5 = -x - 72. 3 - 5x = -9 + x3. Joe’s Canoes charges an initial fee of $20 plus

$4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

4. Write a real-world situation that could be modeled by the equation 500 + 250x = 300x.