Question

How to solve -3-6(4x+6)>-111

Answer 1

since the x is in parentheses, first clear away everything but the parentheses.
-3 -6 (4x + 6) > -111
-6 (4x + 6) > -108
(4x + 6) < 18 (flip the > to < because you divide by a negative number)
now that you have just the parentheses, clear away everything but the x
4x <12
x < 3

Answer 2

Answer:

$-3-6\left(4x+6\right)>-111\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:3\right)\end{bmatrix}$

Step-by-step explanation:

$-3-6\left(4x+6\right)>-111$

$\gray{\mathrm{Add\:}3\mathrm{\:to\:both\:sides}}$

$-3-6\left(4x+6\right)+3>-111+3$

$\gray{\mathrm{Simplify}}$

$-6\left(4x+6\right)>-108$

$\gray{\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}}$

$\left(-6\left(4x+6\right)\right)\left(-1\right)<\left(-108\right)\left(-1\right)$

$\gray{\mathrm{Simplify}}$

$6\left(4x+6\right)<108$

$\gray{\mathrm{Divide\:both\:sides\:by\:}6}$

$\displaystyle\frac{6\left(4x+6\right)}{6}<\frac{108}{6}$

$\gray{\mathrm{Simplify}}$

$4x+6<18$

$\gray{\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}}$

$4x+6-6<18-6$

$\gray{\mathrm{Simplify}}$

$4x<12$

$\gray{\mathrm{Divide\:both\:sides\:by\:}4}$

$\displaystyle\frac{4x}{4}<\frac{12}{4}$

$\gray{\mathrm{Simplify}}$

$x<3$