Question

Solve :
(i) |x $-$ 2| = 6

(ii) |3x $-$ 6| = 21

(iii) |4x $-$ 2| = 10

(iv) |$-$(2x$-$3) | = 7

(v) |x$-$$\frac{1}{2}$| = $\frac{3}{2}$

Answer 1

(i)
$$\begin{gathered} \left|x-2\right|=6 \\ \Rightarrow x-2=6\mathrm{or}x-2=-6 \\ \Rightarrow x=8\mathrm{or}x=-4 \end{gathered}$$

(ii)
$$\begin{gathered} \left|3x-6\right|=21 \\ \Rightarrow 3x-6=21\mathrm{or}3x-6=-21 \\ \Rightarrow 3x=27\mathrm{or}3x=-15 \\ \Rightarrow x=9\mathrm{or}x=-5 \end{gathered}$$

(iii)
$$\begin{gathered} \left|4x-2\right|=10 \\ \Rightarrow 4x-2=10\mathrm{or}4x-2=-10 \\ \Rightarrow 4x=12\mathrm{or}4x=-8 \\ \Rightarrow x=3\mathrm{or}x=-2 \end{gathered}$$

(iv)

$$\begin{gathered} \left|-\left(2x-3\right)\right|=7 \\ \Rightarrow -\left(2x-3\right)=7\mathrm{or}-\left(2x-3\right)=-7 \\ \Rightarrow -2x+3=7\mathrm{or}-2x+3=-7 \\ \Rightarrow 2x=-4\mathrm{or}2x=10 \\ \Rightarrow x=-2\mathrm{or}x=5 \end{gathered}$$

(v)

$$\begin{gathered} \left|x-\frac{1}{2}\right|=\frac{3}{2} \\ \Rightarrow x-\frac{1}{2}=\frac{3}{2}\mathrm{or}x-\frac{1}{2}=-\frac{3}{2} \\ \Rightarrow x=2\mathrm{or}x=-1 \end{gathered}$$