Question

Which represents the solution set to the inequality -1.5(4x + 1) > 4.5 -2.5(x + 1)?

Answer 1

Answer: C

Step-by-step explanation: got it right on edg

Answer 2

The solution set to inequality is:

$\boxed{-1.5\left(4x+1\right)>4.5-2.5\left(x+1\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x$

Solution:

Given inequality is:

$-1.5(4x + 1) > 4.5 -2.5(x + 1)$

We have to find the solution set to inequality

From given,

$-1.5(4x + 1) > 4.5 -2.5(x + 1)\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-1.5\left(4x+1\right)\cdot \:10>4.5\cdot \:10-2.5\left(x+1\right)\cdot \:10\\\\-15\left(4x+1\right)>45-25\left(x+1\right)$

Expand

$-60x -15 > 45 -25x - 25\\\\Simplify\\\\-60x-15>-25x +20$

$\mathrm{Add\:}15\mathrm{\:to\:both\:sides}\\\\-60x-15+15>-25x+20+15\\\\Simplify\\\\-60x>-25x+35\\\\\mathrm{Add\:}25x\mathrm{\:to\:both\:sides}\\\\-60x+25x>-25x+35+25x\\\\Simplify\\\\-35x>35\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-35x\right)\left(-1\right)$

Thus the solution set is:

$-1.5\left(4x+1\right)>4.5-2.5\left(x+1\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x$