Question

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

Answer 1

Given

5|2x + 1| – 3 ≤ 7

Find

Solve the inequality

Step-by-step explanation

`\begin{gathered} 5|2x+1|-3\leq7 \\ 5|2x+1|\leq7+3 \\ 5\lvert2x+1\rvert\leq10 \\ |2x+1|\leq(10)/(5) \\ \\ |2x+1|\leq2 \end{gathered}`

we know that

`2x+1\leq2\text{ }and\text{ }2x+1>-2`

so ,

`\begin{gathered} 2x+1\leq2 \\ 2x\leq1 \\ x\leq(1)/(2) \\ \\ and \\ \\ 2x+1\ge-2 \\ 2x\ge-2-1 \\ 2x\ge-3 \\ x\ge-(3)/(2) \end{gathered}`

so ,

`-(3)/(2)\leq x\leq(1)/(2)`

Final Answer

Hence , the correct option is

`-(3)/(2)\leq x\leq(1)/(2)`