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,

$\begin{gathered} \frac{-2}{4}\leq\frac{4x}{4}\leq\frac{12}{4} \\ -0.5\leq x\leq3 \end{gathered}$

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

$-0.5\leq x\leq3$