Question

5|1-2xl-7 = 3Check your solution

Answer 1

Given:

$5|1-2x|-7=3$

Solve the equation,

$\begin{gathered} 5|1-2x|-7=3 \\ \text{Add 7 on both sides} \\ 5|1-2x|-7+7=3+7 \\ 5|1-2x|=10 \\ \text{Divide by 5 on both sides} \\ \frac{5}{5}|1-2x|=\frac{10}{5} \\ |1-2x|=2 \end{gathered}$

Apply the absolute rule,

$\text{If }|u|=a,a>0\text{ then }u\: =\: a\text{ or }u\: =\: -a$

It gives,

$\begin{gathered} 1-2x=-2\text{ or }1-2x=2 \\ -2x=-3\text{ or }-2x=1 \\ x=\frac{3}{2}\text{ or }x=-\frac{1}{2} \end{gathered}$

Check the solution,

$\begin{gathered} \text{for x=}\frac{3}{2} \\ \text{Take the left and side of the equation,} \\ 5|1-2x|-7=5|1-2(\frac{3}{2})|-7 \\ =5|1-3|-7 \\ =5|-2|-7 \\ =5\cdot2-7\ldots\text{.. since |-x|=x} \\ =10-7 \\ =3 \\ =\text{ right-hand side} \end{gathered}$

And,

$\begin{gathered} \text{For x=}\frac{-1}{2} \\ 5|1-2x|-7=5|1-2(\frac{-1}{2})|-7 \\ =5|1+1|-7 \\ =10-7 \\ =3 \end{gathered}$

Answer:

$x=\frac{3}{2}\text{ or }x=-\frac{1}{2}$