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]
