91Ó°ÊÓ

The absolute value or modulus of a real number x, denoted $\left|x\right|$, it is the non-negative value of $x$without regard to its sign.

$\left|x\right|=x$if$x$ is positive,

$\left|x\right|=−x$if$x$ is negative,

$\left|0\right|=0$.

For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.

We are given the expression$|−4w+2|=14$ assuming a positive value for the modulus expression we get:

role="math" localid="1643046058341" $\begin{array}{l}−4w+2=14\\ −4w+2−2=14−2\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„}\left[\text{²õ³Ü²ú³Ù°ù²¹³¦³Ù }2\text{ f°ù´Ç³¾}both\text{ }sides\right]\\ −4w=12\\ w=\frac{12}{−4}\\ w=−3\end{array}$

Thus$w=−3$ is one of the solutions.

$\begin{array}{l}−4w+2=−14\\ −4w+2−2=−14−2\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„}\left[\text{²õ³Ü²ú³Ù°ù²¹³¦³Ù }2\text{ f°ù´Ç³¾}both\text{ }sides\right]\\ −4w=−16\text{ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„ â¶Ä„â¶Ä„â¶Ä„â¶Ä„â¶Ä„  }\left[\text{»å¾±±¹¾±»å±ð b²â-}4\text{ f°ù´Ç³¾}both\text{ }sides\right]\\ \frac{−4w}{−4}=\frac{−16}{−4}\\ w=4\end{array}$

Thus$w=4$ is one of the solutions.

The solution set is $\{−3,4\}$, we graph these values on the number line as shown below: