Solve each equation in Exercises 96–102 by the method of your choice. -4|x+1| + 12 = 0

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is denoted as |x|, which equals x if x is non-negative and -x if x is negative. Understanding absolute value is crucial for solving equations that involve expressions within absolute value bars, as it leads to two possible cases to consider.

Linear Equations

A linear equation is an equation of the first degree, meaning it involves variables raised only to the power of one. The general form is ax + b = c, where a, b, and c are constants. In the context of the given equation, once the absolute value is isolated, it can be transformed into linear equations that can be solved for the variable x.

Isolating the Variable

Isolating the variable is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable on one side and the constants on the other. In the case of the given equation, isolating the absolute value expression is the first step to simplifying the problem and finding the solution for x.