Question

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

1/8(40x+16)=9x−7(2x−1)−5 5x+2=9x−14x+7−5 5x+2=5x+2 2=2


the student solved the equation _______________ because the original equation has ___________ solution(s).


Select the options that makes the above statements true.


Question 5 options:


correctly



incorrectly



no solution



one solution



infinitely many solutions

Answer 1

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

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

Answer 2

Incorrectly , one solution

Explanation:

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

Given equation,

`(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).