Question

HELPPP!!!!!!!!!!!!!!!! PLEASE! :D

Answer 1

Answer:

The solution to the inequality is:

$-1\le \:x\le \:3$

The line graph of the solution is also attached.

Step-by-step explanation:

Given the expression

$4x-1\:\le \:5x\:\le \:3\left(x+2\right)$

solving the expression

$4x-1\:\le \:5x\:\le \:3\left(x+2\right)$

• $\mathrm{If}\:a\le \:u\le \:b\:\mathrm{then}\:a\le \:u\quad \mathrm{and}\quad \:u\le \:b$

$4x-1\le \:5x\quad \mathrm{and}\quad \:5x\le \:3\left(x+2\right)$

solving

$4x-1\le \:5x$

Add 1 to both sides

$4x-1+1\le \:5x+1$

Simplify

$4x\le \:5x+1$

Subtract 5x from both sides

$4x-5x\le \:5x+1-5x$

simplify

$-x\le \:1$

Multiply both sides by -1 (reverse inequality)

$\left(-x\right)\left(-1\right)\ge \:1\cdot \left(-1\right)$

Simplify

$x\ge \:-1$

Similarly solving

$5x\le \:3\left(x+2\right)$

Subtract 3x from both sides

$5x-3x\le \:3x+6-3x$

Simplify

$2x\le \:6$

Divide both sides by 2

$\frac{2x}{2}\le \frac{6}{2}$

Simplify

$x\le \:3$

So combine the interval

$x\ge \:-1\quad \mathrm{and}\quad \:x\le \:3$

Merge overlapping intervals

$-1\le \:x\le \:3$

Therefore, the solution to the inequality is:

$-1\le \:x\le \:3$

The line graph of the solution is also attached.