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} \\ (5)/(5)|1-2x|=(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=(3)/(2)\text{ or }x=-(1)/(2) \end{gathered}`

Check the solution,

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

And,

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

Answer:

`x=(3)/(2)\text{ or }x=-(1)/(2)`