Chapter H, Problem 1DE

Solve: $\left|x\right|=6$. Then graph on the number line.

To determine

To calculate: The solution of the equation $\left|x\right|=6$ and graph the solution on the number line.

Answer to Problem 1DE

Solution:

The solution set for the provided equation is $\left\{-6,6\right\}$.

Explanation of Solution

Given Information:

The equation $\left|x\right|=6$

Formula Used:

If p is a positive number and X is any algebraic expression, then following three cases arise:

Case 1: If the equation $\left|X\right|=p$ is of this type than it satisfy either $X=-p$ or $X=p$.

Case 2: If the equation $\left|X\right|=0$ is of this type than it satisfies the equation $X=0$.

Case 3: If the equation $\left|X\right|=-p$ is of this type than it has no solution.

Calculation:

Consider the equation with absolute value,

$\left|x\right|=6$

The given equation is of the form $\left|X\right|=p$. The solutions of $\left|X\right|=p$ satisfy either $X=-p$ or $X=p$. So, the solutions of the given equation $\left|x\right|=6$ will satisfy any of following two equations

$x=6$ or $x=-6$

Consider equation $x=6$. The solution of the equation $x=6$ is number 6.

Consider equation $x=-6$. The solution of the equation $x=-6$ is number $-6$.

Thus, the solution set of the provided equation $\left|x\right|=6$ is $\left\{-6,6\right\}$.

The graph for the given equation on the number line is shown below,

Therefore, the solution set for the provided equation is $\left\{-6,6\right\}$.