#### Answer

The solution is $\Big[-\dfrac{11}{5},\infty\Big)$

#### Work Step by Step

$\dfrac{4x+7}{-3}\le2x+5$
Change the sign of the denominator and the sign of the numerator on the left side:
$\dfrac{-4x-7}{3}\le2x+5$
Take $3$ to multiply the right side:
$-4x-7\le3(2x+5)$
$-4x-7\le6x+15$
Take $6x$ to the left side and $7$ to the right side:
$-4x-6x\le15+7$
$-10x\le22$
Rearrange:
$10x\ge-22$
Take $10$ to divide the right side and simplify:
$x\ge-\dfrac{22}{10}$
$x\ge-\dfrac{11}{5}$
Expressing the solution in interval notation:
$\Big[-\dfrac{11}{5},\infty\Big)$