What is the solution set of the equation |2x+3|=7 in the set of rational numbers? A, {4,-10}

B, {5,-2}

C. {4,5}

D. {-5,2}

d

Step-by-step explanation:

-10=-5*2;        4=2*2

l-10+3l= 7;      l4+3l=7

Work Shown:

|2x+3| = 7 means either 2x+3 = 7 or 2x+3 = -7

Solve each for x

2x+3 = 7

2x = 7-3

2x = 4

x = 4/2

x = 2 is one solution

Repeat for the other equation

2x+3 = -7

2x = -7-3

2x = -10

x = -10/2

x = -5 is the other solution

Each solution can be checked by plugging it back into the original equation and simplifying. You should get the same number on both sides

For instance, checking x = -5 leads to

|2x+3| = 7

|2(-5)+3| = 7

|-10+3| = 7

|-7| = 7

7 = 7

Which confirms x = -5. I'll let you check x = 2.