Question

`|4x - 5 \leqslant 7|`here's my absolute value equation

Answer 1

2.

The inequation is given as,

`\lvert4x-5\rvert\leq7`

Consider the analogy,

`\lvert a\rvert\leq b\Rightarrow-b\leq a\leq b`

Applying this analogy to the given inequality,

`-7\leq4x-5\leq7`

Now, we just need to obtain the solution set for this inequality.

Add 5 to each term,

`\begin{gathered} -7+5\leq4x-5+5\leq7+5 \\ -2\leq4x\leq12 \end{gathered}`

Divide by 4 each term of the inequality,

`\begin{gathered} (-2)/(4)\leq(4x)/(4)\leq(12)/(4) \\ -0.5\leq x\leq3 \end{gathered}`

Thus, the solution set to the given inequation is obtained as,

`-0.5\leq x\leq3`