Question

Which of the inequalities has the solution whose graph is shown?

F. $2x+10<16$

G. $-4x-5<7$

H. $-3x+8<-1$

I. $4-2x>10$

Short answer

The correct equation is option G.

Step-by-step solution

Step 1.  Apply the concept of Linear Inequalities

In this, use the concept of solving the linear inequalities by doing mathematical operations.

Step 2.  Finding the correct solution

Here,

First expression is $2x+10<16$.

$\begin{array}{l}2x+10<16\\ 2x+10-10<16-10\\ 2x<6\\ \frac{2x}{2}<\frac{6}{2}\\ x<3\end{array}$

Second Expression is $-4x-5<7$

$\begin{array}{l}-4x-5<7\\ -4x-5+5<7+5\\ -4x<12\\ \frac{-4x}{-4}<\frac{12}{-4}\\ x>-3\end{array}$

Third expression is $-3x+8<-1$.

$\begin{array}{l}-3x+8<-1\\ -3x+8-8<-1-8\\ -3x<-9\\ \frac{-3x}{-3}<\frac{-9}{-3}\\ x>3\end{array}$

Fourth expression is $4-2x>10$.

$\begin{array}{l}4-2x>10\\ 4-2x-4>10-4\\ -2x>6\\ \frac{-2x}{-2}>\frac{6}{-2}\\ x<-3\end{array}$

Now, from the above four solved expression, it is clearly seen that the correct solution for the graph is second expression whose solution is $x>-3$.

Step 3.  Eliminating the options to get correct one

F. $2x+10<16$:It is not the correct option because it’s solution is$x<3$ which is different from the correct solution that is $x>-3$.

G. $-4x-5<7$: It is the correct option because it’s solution is $x>-3$ which is same from the correct solution that is $x>-3$.

H. $-3x+8<-1$: It is not the correct option because it’s solution is $x>3$ which is different from the correct solution that is $x>-3$.

I. $4-2x>10$: It is not the correct option because it’s solution is $x<-3$ which is different from the correct solution that is $x>-3$.