Question

What is the solution of 2|2x-1|-8=18?

Answer 1

    ➣ Assignment: $\bold{Solve \ Equation: \ 2\left|2x-1\right|-8=18}$

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       ➣ Answer: $\boxed{\bold{x=-6, \ x=7}}$

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Explanation: ↓↓↓↓↓

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       ➤ [ Step One ] Add 8 To Both Sides

$\bold{2\left|2x-1\right|-8+8=18+8}$

       ➤ [ Step Two ] Simplify

$\bold{2\left|2x-1\right|=26}$

       ➤ [ Step Three ] Divide Both Sides By 2

$\bold{\frac{2\left|2x-1\right|}{2}=\frac{26}{2}}$

       ➤ [ Step Four ] Simplify

$\bold{\left|2x-1\right|=13}$

       ➤ [ Step Five ] Apply Absolute Rule

Note: $\bold{Absolute \ Rule: \ \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a}$

$\bold{2x-1=-13\quad \mathrm{or}\quad \:2x-1=13}$

       ➤ [ Step Six ] Simplify Equations

$\bold{2x-1=-13: \ x=-6}$

$\bold{2x-1=13: \ x \ = \ 7}$

       ➤ [ Step Seven ] Combine Solutions

$\bold{x=-6, \ x=7}$

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$\bold{\rightarrow Mordancy \leftarrow}$

Answer 2

Solve for $|2x-1|$:

$2|2x-1|-8=18\implies2|2x-1|=26\implies|2x-1|=13$

Now if $2x-1\ge0$, we have $|2x-1|=2x-1$ and

$2x-1=13\implies2x=14\implies x=7$

On the other hand, if $2x-1$, then $|2x-1|=-(2x-1)=1-2x$ and

$1-2x=13\implies-2x=12\implies x=-6$