Page 203 - ABCTE Study Guide_Neat

• Horizontal lines have a slope of zero (m = 0). Vertical lines have an undefined slope.
• Parallel lines have the same slope. The slopes of perpendicular lines are negative
reciprocals of each other.
• Linear inequalities look the same as linear equations, except that a region above or
below the line (solid or dashed) is shaded to show the area included in the solution.
• In a system of equations, a pair of linear equations has a single solution at the point
where the two lines intersect, unless the lines are parallel, in which case there is no solution.

Absolute Value Equations & Inequalities

Lesson Objective

In the upcoming sections, we'll review the concept of absolute values and discuss absolute-value equations.
We'll also cover absolute-value inequalities and compound inequalities.

Previously Covered

• In the section above, we reviewed linear equations, slopes, and linear inequalities.
• Additionally, we practiced creating graphs based on these concepts and creating
equations based on given graphs.

Absolute Value Equations

Absolute value is the distance between a number and zero on a number line. Since absolute value
represents a distance, its result is always positive. The symbol for absolute value is a pair of bars around
the variable or number: . Absolute value is often used in situations where answers involve a range of
numbers.

First, look at this very simple absolute value equation:

On a number line, it would like this:

The answer to this equation is x = 3 or x = -3. These are the two values that would make the equation
true, since taking the absolute value of a negative number gives a positive result.

There is no solution to the problem since there are no numbers that you can put in place of x to
make an answer of -4.

To solve absolute value equations, be sure to get the absolute value alone on one side of the equation.