Question

1. which equation has a solution of x = 4?

a. 2x + 5 = 4x + 6
b. x + 5 = 4x + 5
c. 4x + 5 = 3x + 6
d. 4x + 4 = 3x + 8

Explanation:

Step1: Test option a

Substitute \( x = 4 \) into \( 2x + 5 = 4x + 6 \).
Left side: \( 2(4)+5 = 8 + 5 = 13 \).
Right side: \( 4(4)+6 = 16 + 6 = 22 \).
Since \( 13
eq22 \), option a is wrong.

Step2: Test option b

Substitute \( x = 4 \) into \( x + 5 = 4x + 5 \).
Left side: \( 4 + 5 = 9 \).
Right side: \( 4(4)+5 = 16 + 5 = 21 \).
Since \( 9
eq21 \), option b is wrong.

Step3: Test option c

Substitute \( x = 4 \) into \( 4x + 5 = 3x + 6 \).
Left side: \( 4(4)+5 = 16 + 5 = 21 \).
Right side: \( 3(4)+6 = 12 + 6 = 18 \).
Since \( 21
eq18 \), option c is wrong.

Step4: Test option d

Substitute \( x = 4 \) into \( 4x + 4 = 3x + 8 \).
Left side: \( 4(4)+4 = 16 + 4 = 20 \).
Right side: \( 3(4)+8 = 12 + 8 = 20 \).
Since \( 20 = 20 \), option d is correct.

Answer:

d. \( 4x + 4 = 3x + 8 \)