Question

A student's work to solve an equation is shown.

Answer 1

Answer:

Incorrectly , one solution

Step-by-step explanation:

The final solution of student is 2 = 2 which is a true statement, i.e. equation has infinitely many solution,

Given equation,

$\frac{1}{8}(40x+16)=9x-7(2x-1) -5$

$5x + 2 = 9x - 14x + 7 -5$ ( by distributive property )

$5x + 2 = -5x +2$

$5x + 5x = 2 - 2$

$10x = 0$

$\implies x = 0$

Hence, the equation has a solution which is 0.

Therefore, the student solved the equation incorrectly because the original equation has one solution(s).

Answer 2

Answer:

the student solved the equation incorrectly because the original equation has one solution

Step-by-step explanation:

1/8(40x + 16) = 9x − 7(2x − 1) − 5

use the distributive property a(b + c) = ab + ac

(1/8)(40x) + (1/8)(16) = 9x + (-7)(2x) + (-7)(-1)

5x +2 = 9x − 14x + 7 − 5       combine like terms

5x + 2 = (9x - 14x) + (7 - 5)

here the student make mistake 9x - 14x = 5x

5x+2=-5x+2    add 5x to both sides and subtract 2 from both sides

5x + 5x + 2 - 2 = -5x + 5x + 2 - 2

10x = 0          divide both sides by 10

10x/10 = 0/10

x = 0