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. Move all terms involving the variable to one side of the equation. 2. Move constant terms to the other side. 3. Simplify and solve for the variable.

Front

Solve for x: 10x + 9 = 4x - 9

Back

x = -3

Front

Write an equation for the following situation: Mary has two job offers with different salaries and raises.

Back

36,000 + 1,500x = 29,000 + 2,500x

Front

Solve for k: -5k + 10 = -2k - 14

Back

k = 8

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 easier to solve.

Front

Write an equation to represent the situation: Celebrity A has 400 followers and gains 75 daily, while Celebrity B has 1,000 followers and loses 25 daily.

Back

400 + 75x = 1,000 - 25x

Front

What is a constant in an equation?

Back

A fixed value that does not change, such as numbers like 9 or 36,000.

Front

What is the first step in solving the equation 3x + 5 = 2x + 10?

Back

Subtract 2x from both sides to get x + 5 = 10.

Front

What is the solution to the equation 2(x - 3) = 4?

Back

x = 7