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

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value of the variable that makes the equation true.

Front

What is the first step in solving the equation 4x + 1 = 7x - 5?

Back

The first step is to get all terms involving x on one side and constant terms on the other side.

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

The solution is x = 2.

Front

What is the significance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides of the equation have the same value.

Front

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

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is a coefficient in a linear equation?

Back

A coefficient is a numerical factor that multiplies a variable in an equation.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you solve the equation 32 - 7x = -6(x + 3)?

Back

First, distribute -6 to get 32 - 7x = -6x - 18, then isolate x to find x = 50.