Question

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

Answer 1

➣ Assignment:
`\bold2x-1\right`

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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

`\bold2\left`

➤ [ Step Two ] Simplify

`\bold2\left`

➤ [ Step Three ] Divide Both Sides By 2

`\bold2x-1\right`

➤ [ Step Four ] Simplify

`\bold=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<0`, then
`|2x-1|=-(2x-1)=1-2x` and

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