Question

Which graph represents the solution set of this inequality? -2x + 7 < 23−2x+7<23

Answer 1

Answer:

The graph and the number line in the attached figure

Step-by-step explanation:

we have

$-2x+7 < 23$

Solve for x

subtract 7 both sides

$-2x+7-7 < 23-7$

$-2x < 16$

Divide by -2 both sides

Remember

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

so

$x > -8$

The solution is the interval (-8,∞)

All real numbers greater than -8

In a number line the solution is the shaded area at right of x=-8 (open circle)

The graph and the number line in the attached figure

Answer 2

Answer:

Step-by-step explanation:

Find the graph attached below

Given the inequality

-2x + 7 < 23−2x+7<23

Simplifying the inequality

-2x+7-7<23-2x+7-7<23-7

-2x<23-2x<16

Subtracting 23 from all sides

-23x-23<-2x<-7

Dividing through by -2

-23x-23/-2 < x < 7/2

Solving -23x-23/-2< x

x > -23x-23/-2

-2x < -23x-23

-2x+23x <-23

21x<-23

x<-23/21

The solution to the inequality are x<-23/21 and x<7/2