Absolute Value Equations

SEI.3.AC.1SLE 1: Solve, with and without appropriate technology, multi-step equations and inequalities with

rational coefficients numerically, algebraically and graphically

Students will be able to solve absolute value equations and inequalities, and be able to graph them.

FHS Equations and Inequalities 2

Absolute Value

• All integers are composed of two parts – the size and the direction. For example, +5 is five units in the positive direction; –5 is five units in the negative direction.

• The absolute value {written like this: }of a number gives the size of the number without the direction. For example, = 5 and = 5. The answer is always positive.

• Conversely, if you have an equation , the answer could be 5 or –5. You will have 2 answers.

55

5

x 5

FHS Equations and Inequalities 3

Absolute Value Equations

To solve absolute value equations, we follow the same procedures that we do in solving any equation.

Solve for the absolute value first. Set up the two solutions, and solve them for the variable.

Here are some examples:3 7x 3 3

3 2 6x

4x 3 8 3 8 x or x

3 8x 2 2

4 4x or x 11 5 x or x