Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable (usually x) that makes the equation true.

Front

What is the first step in solving the equation 6x + 40 = 88?

Back

Subtract 40 from both sides to isolate the term with x.

Front

If the area of a rectangle is given by the equation 6x + 40 = 88, how do you find x?

Back

First, subtract 40 from both sides to get 6x = 48, then divide both sides by 6 to find x = 8.

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter P of a rectangle is given by the formula P = 2(length + width).

Front

If the perimeter of a rectangle is 42 inches, and one side is x inches, how can you express the other side?

Back

If the other side is y inches, then the equation is 2(x + y) = 42.

Front

What is the solution to the equation 3x - 9 = 0?

Back

Add 9 to both sides to get 3x = 9, then divide by 3 to find x = 3.

Front

How do you check if your solution to a linear equation is correct?

Back

Substitute the value of the variable back into the original equation to see if both sides are equal.

Front

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

Back

Isolating a variable means to manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 2x + 5 = 15?

Back

Subtract 5 from both sides to get 2x = 10, then divide by 2 to find x = 5.