Question

Sarita showed the steps to solving the equation.

5 (x minus 3) + 7 (x + 4) = 73
Steps
Sarita’s Solution
Sarita’s Verification
1
5 x minus 15 + 7 x + 28 = 73
5 (5 minus 3) + 7 (5 + 4) = 73. 5 (negative 2) + 7 (9) = 73. Negative 10 + 63 = 73. 53 not-equal-to 73.
2
(5 + 7) x + (negative 15 + 28) = 73
3
12 x + 13 = 73
4
12 x + 60
5
x = 5

When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?
Sarita’s solution is correct. She made an error in her verification.
Sarita was supposed to add the 5 and 7 in the first step.
Sarita added +13 instead of Negative 13 in the fourth step.
Sarita was supposed to use the division property of equality in the third step.

Answer 1

Answer: Sarita’s solution is correct. She made an error in her verification.

Why: The algebra steps are right (5x−15+7x+28 → 12x+13 → 12x = 60 → x = 5). In her check she computed 5−3 = −2 by mistake. Correct check:
5(5−3)+7(5+4) = 5(2)+7(9) = 10+63 = 73, which matches.