Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you solve an equation with variables on both sides?

Back

1. Simplify both sides if necessary. 2. Move all variable terms to one side and constant terms to the other. 3. Combine like terms. 4. Isolate the variable.

Front

Solve for x: 4(1-x) = -2(x+1)

Back

x = 3

Front

What does the equation 100 – 2x = 140 – 6x represent?

Back

It represents a situation where Tank A has 100 gallons of water and loses 2 gallons per hour, while Tank B has 140 gallons and loses 6 gallons per hour. It asks when both tanks will have the same amount of water.

Front

Solve for x: 5x - 14 = 8x + 4

Back

x = -6

Front

Write an equation for the cost of trophies with engraving at two different stores: Store A: $12.50 + $0.40 per letter, Store B: $14.75 + $0.25 per letter.

Back

12.50 + 0.40x = 14.75 + 0.25x

Front

Solve for t: 30 + 6t = 11t

Back

t = 6

Front

What is the first step in solving an equation with variables on both sides?

Back

Identify and simplify both sides of the equation if necessary.

Front

What does it mean to isolate a variable in an equation?

Back

To manipulate the equation so that the variable is alone on one side, making it easy to determine its value.

Front

What is a like term in an equation?

Back

Terms that have the same variable raised to the same power, which can be combined.