Solving Linear Equations and Inequalities

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 that makes the equation true.

Front

What is the difference between an open circle and a closed circle on a number line?

Back

An open circle indicates that the number is not included in the solution (e.g., x < 6), while a closed circle indicates that the number is included (e.g., x ≤ 6).

Front

How do you graph the inequality b < 6?

Back

You would use an open circle at 6 and shade to the left to indicate all numbers less than 6.

Front

What does the inequality 6 > x mean?

Back

It means that x is less than 6.

Front

How do you isolate a variable in an equation?

Back

You perform inverse operations to both sides of the equation to get the variable by itself.

Front

What is the first step in solving the equation 2x + 10 = 22?

Back

Subtract 10 from each side to begin isolating the variable.

Front

What is the solution to the equation 4(2x - 3) = 6x + 2?

Back

x = 7.

Front

What does the inequality -8b - 8 > 56 imply about b?

Back

It implies that b < -8.

Front

What is the purpose of checking your solution in an equation?

Back

To verify that the value you found satisfies the original equation.