Question

Solve each equation. Check the solution.

$2\left|\text{w}+6\right|=10$

Short answer

The value of $\text{w}$ is$-\mathbf{1}$ and $-\mathbf{11}$.

Step-by-step solution

- State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

- Solve the inequality.

If x is a number, then absolute value of x is written as $\left|x\right|$.

Here, the inequality is:

$2\left|w+6\right|=10$

Case 1:

$\begin{array}{c}a=b\\ 2\left(w+6\right)=10\\ 2w+12=10\\ 2w+12-12=10-12\\ 2w=-2\\ w=-1\end{array}$

Or Case 2:

$\begin{array}{c}a=-b\\ 2\left(w+6\right)=-10\\ 2w+12=-10\\ 2w+12-12=-10-12\\ 2w=-22\\ w=-11\end{array}$

The solution is $-1$and $-11$

- Check the solution.

For case 1: $w=-1$.

Check:

$\begin{array}{r}2\left|w+6\right|=10\\ 2\left|-1+6\right|=10\\ 2\left|5\right|=10\\ 2\times 5=10\\ 10=10\end{array}$

Thus, it is correct.

For case 2: $w=-11$.

Check:

$\begin{array}{r}2\left|w+6\right|=10\\ 2\left|-11+6\right|=10\\ 2\left|-5\right|=10\\ 2\times 5=10\\ 10=10\end{array}$

Thus, it is also correct.

- State the conclusion.

Therefore, the solution set for $w$ is $\left\{-1,-11\right\}$.