Question

current learning objective: solving an absolute value equation
question 7
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solve the absolute value equation for (x).
(left|\frac{x}{4}+10
ight| = 7) then (x=) enter your answer
enter your solution(s) as integers or reduced fractions separated by commas. enter d
submit answer
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Explanation:

Step1: Recall absolute - value property

If \(|a| = b\) (\(b\geq0\)), then \(a = b\) or \(a=-b\). So for \(|\frac{x}{4}+ 10| = 7\), we have \(\frac{x}{4}+10 = 7\) or \(\frac{x}{4}+10=-7\).

Step2: Solve \(\frac{x}{4}+10 = 7\)

Subtract 10 from both sides: \(\frac{x}{4}=7 - 10=-3\). Then multiply both sides by 4 to get \(x=-3\times4=-12\).

Step3: Solve \(\frac{x}{4}+10=-7\)

Subtract 10 from both sides: \(\frac{x}{4}=-7 - 10=-17\). Then multiply both sides by 4 to get \(x=-17\times4=-68\).

Answer:

\(x=-12,-68\)