Which equation has x = 14 as a solution?

• A. 2x + 7 = x + 21
• B. 4x - 9 = 7
• C. 3x + 5 = 2x + 9
• D. x - 7 = x + 7

Answer: (A)

When a number is a solution to a linear equation, plugging that number in for x makes both sides the same value. So, to check if 14 works, substitute x with 14 in each equation and see if the two sides match.

For the first equation: 2x + 7 on the left becomes 2(14) + 7 = 28 + 7 = 35. The right side is x + 21 = 14 + 21 = 35. Both sides are equal, so 14 satisfies this equation.

Check the others by the same idea: in the second equation, 4x − 9 becomes 4(14) − 9 = 56 − 9 = 47, while the right side is 7; they don’t match. The third equation gives 3x + 5 = 3(14) + 5 = 42 + 5 = 47 on the left, and 2x + 9 = 2(14) + 9 = 28 + 9 = 37 on the right; they don’t match either. In the fourth, x − 7 = 14 − 7 = 7 on the left, while x + 7 = 14 + 7 = 21 on the right; not equal.

Only the first equation holds true when x = 14, so that equation is the one that has 14 as a solution.