BlakelynU122896 BlakelynU122896
  • 25-10-2022
  • Mathematics
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I need to solve the absolute value inequality and write interval notation for the solution set?

I need to solve the absolute value inequality and write interval notation for the solution set class=

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AnesaG65058 AnesaG65058
  • 25-10-2022

Given:

The inequality is,

[tex]|2x-6|\leq14[/tex]

Simplify the inequality,

[tex]\begin{gathered} |2x-6|\leq14 \\ \text{Apply the absolute rule, If |a|}\leq u\text{ Then -u}\leq a\leq u \\ -14\leq(2x-6)\leq14 \\ -14+6\leq2x\leq14+6 \\ -8\leq2x\leq20 \\ -\frac{8}{2}\leq x\leq\frac{20}{2} \\ -4\leq x\leq10 \end{gathered}[/tex]

Answer: The solution set is [-4,10].

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