Question

Solve the two step inequality and match the answer to the graph.

Answer 1

SOLVING THE INEQUALITY  $3x-10<-25$ TO MATCH OPTION A

Considering the inequality

$3x-10<-25$

$3x-10+10<-25+10$

$3x<-15$

$\frac{3x}{3}<\frac{-15}{3}$

$x<-5$

Thus,

$3x-10<-25\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-5\right)\end{bmatrix}$

Therefore, the inequality $3x-10<-25$ has the solution $x<-5$ which matches the option A.

SOLVING THE INEQUALITY  $-4x+7\ge \:27$  TO MATCH OPTION B

Considering the inequality

$-4x+7\ge \:27$

$-4x+7-7\ge \:27-7$

$-4x\ge \:20$

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

$\left(-4x\right)\left(-1\right)\le \:20\left(-1\right)$

$4x\le \:-20$

$\frac{4x}{4}\le \frac{-20}{4}$

$x\le \:-5$

Thus,

$-4x+7\ge \:27\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-5\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-5]\end{bmatrix}$

Therefore, the inequality  $-4x+7\ge \:27$ has the solution $x\le \:-5$ which matches the option B.

SOLVING THE INEQUALITY  $\frac{x}{1}-9<-10$  TO MATCH OPTION C

Considering the inequality

$\frac{x}{1}-9<-10$

$\mathrm{Apply\:rule}\:\frac{a}{1}=a$

$x-9<-10$     ∵  $\frac{x}{1}=x$

$x-9<-10$

$x-9+9<-10+9$

$x<-1$

$\frac{x}{1}-9<-10\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\end{bmatrix}$

Therefore, the inequality $\frac{x}{1}-9<-10$ has the solution $x<-1$ which matches the option C.

SOLVING THE INEQUALITY $5\left(x-2\right)>-15$ TO MATCH OPTION D

Considering the inequality

$5\left(x-2\right)>-15$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left(x-2\right)}{5}>\frac{-15}{5}$

$x-2>-3$

$x-2+2>-3+2$

$x>-1$

Thus,

$5\left(x-2\right)>-15\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-1,\:\infty \:\right)\end{bmatrix}$

Therefore, the inequality $5\left(x-2\right)>-15$ has the solution $x>-1$ which matches the option D.