Solving Linear and Absolute Value Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = 0, where a and b are constants.

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression. It is of the form |x| = a, where a is a non-negative number.

Front

How do you solve the equation |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

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

Back

Isolating the variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the first step in solving the equation 10x - 6x = 23 + 5?

Back

The first step is to combine like terms on both sides of the equation.

Front

What is the solution to the equation −2|−2r − 4| = -12?

Back

The solutions are r = -5 and r = 1.

Front

How do you handle negative coefficients in absolute value equations?

Back

You can factor out the negative coefficient and then solve the resulting absolute value equation.

Front

What is the solution to the equation l 4x−3 l = 17?

Back

The solutions are x = 5 and x = -3.5.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you simplify the expression 6(x - 2)?

Back

You apply the distributive property: 6(x - 2) = 6x - 12.