Answered

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What is the solution of 5|2x + 1| – 3 ≤ 7?

What Is The Solution Of 52x 1 3 7 class=

Sagot :

Given

5|2x + 1| – 3 ≤ 7

Find

Solve the inequality

Explanation

[tex]\begin{gathered} 5|2x+1|-3\leq7 \\ 5|2x+1|\leq7+3 \\ 5\lvert2x+1\rvert\leq10 \\ |2x+1|\leq\frac{10}{5} \\ \\ |2x+1|\leq2 \end{gathered}[/tex]

we know that

[tex]2x+1\leq2\text{ }and\text{ }2x+1>-2[/tex]

so ,

[tex]\begin{gathered} 2x+1\leq2 \\ 2x\leq1 \\ x\leq\frac{1}{2} \\ \\ and \\ \\ 2x+1\ge-2 \\ 2x\ge-2-1 \\ 2x\ge-3 \\ x\ge-\frac{3}{2} \end{gathered}[/tex]

so ,

[tex]-\frac{3}{2}\leq x\leq\frac{1}{2}[/tex]

Final Answer

Hence , the correct option is

[tex]-\frac{3}{2}\leq x\leq\frac{1}{2}[/tex]

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