Question

Solve for x: 2|x − 3| + 1 = 7

Answer 1

`\huge\boxed{x=6\ \vee\ x=0}`

Explanation:

`2|x-3|+1=7\qquad\text{subtract 1 from both sides}\\\\2|x-3|+1-1=7-1\\\\2|x-3|=6\qquad\text{divide both sides by 2}\\\\(2|x-3|)/(2)=(6)/(2)\\\\|x-3|=3`

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`|a|=\left\{\begin{array}{ccc}a&\text{for}&a\geq0\\-a&\text{for}&a<0\end{array}\righ`

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Therefore

`|x-3|=3\iff x-3=3\ \vee\ x-3=-3\qquad\text{add 3 to both sides}\\\\x-3+3=3+3\ \vee\ x-3+3=-3+3\\\\\boxed{x=6\ \vee\ x=0}`