Question

Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below.

(1 – 3x) = 4(– + 2)
4 lines of math. The first line is, StartFraction 5 Over 6 EndFraction left-parenthesis 1 minus 3 x right-parenthesis equals 4 left-parenthesis negative StartFraction 5 x Over EndFraction plus 2 right-parenthesis. The second line is, StartFraction 5 Over 6 EndFraction minus StartFraction 5x Over 2 EndFraction equals StartFraction 5x Over 2 EndFraction plus 8. The third line in plus StartFraction 5x Over 2 EndFraction and StartFraction 5x Over 2 EndFraction on both sides of the equal sign. The fourth line is 0 equals x.

0 = x
Which statement is true about Micah’s solution?

Micah’s solution is wrong. There are no values of x that make the statement true.
Micah’s solution is correct, and the value of x that makes the statement true is 0.
Micah should have divided by StartFraction 5 Over 2 EndFraction.
Micah should have subtracted StartFraction 5 Over 2 EndFraction.

Answer 1

Can you rewrite the original work, or maybe take a screenshot of it?

5/6 (1- 3x) = 4(?? + 2)

Not able to understand the huge wall of text

Answer 2

yes

Answer 3

I'll delete that because it has your name in it. Want you to stay safe

Answer 4

okay thank you

Answer 5

So his work seems probably complex because it has fractions but it's not anything too crazy

Answer 6

so how do i do it? its confusing im not the best when it comes to word problems

Answer 7

Basically they want us to make sure if he did it correct

So we have

5/6 (1-3x) = 4(-5x/8 + 2)

So let's work on the left hand side

Let's distribute that 5/6, what do you get?

Answer 8

i dont know how to distribut a fraction that easily

Answer 9

no worries, it's pretty simple actually, but we do have to simplicity it

(5/6 * 1) - (5/6 * 3x)

What is anything times 1?
5 times 1 = ?
19372838 times 1 = ?
So what is
5/6 * 1 = ?

Answer 10

5/6

Answer 11

5/6 - 5/2x

Answer 12

Perfecto,

And then
\(\frac{5}{6} \times 3x\)

Answer 13

Ayyy you're a math whiz and you don't even know it!

But just to be a little careful, that x is in the numerator (the top half of the fraction)

So it's better to write it as
5x/2

Answer 14

mk

Answer 15

Now to do the other side quickly

4\(\left(\frac{-5x}{8} + 2\right)\)

Answer 16

thats where i got stuck

Answer 17

So we just multiply 4 across

\(4 \times\frac{-5x}{8}\) + (4*2)

You can do what you did for the other question, the 8 in the denominator becomes 2 and the 4 becomes a 1

Answer 18

-5/2+8

Answer 19

You accidentally dropped the x haha

So now we have

5/6 - 5x/2 = -5x/2 + 8

And you can see that's also what Micah got so far.

Now we need to add 5x/2 on both sides
If the fraction scares you, think of 5x/2 as an apple and so we have
- apple = - apple

What happens when you add an apple on both sides? It disappears!

So what do you get then?

Answer 20

5/6=8

Answer 21

And is that a no solution or a one solution?

Answer 22

no solution

Answer 23

Perfect! And Micah thought x = 0

So is he wronggg or what? What do you think the answer is then

Answer 24

the first one?

Answer 25

Absolutely correct! Well done Payton :D

Answer 26

i try

Answer 27

You're doing fantastic

Answer 28

even tho this assignment is killing me?

Answer 29

What doesn't kill you, makes you stronger!

Answer 30

stand a little taller

Answer 31

At ease, soldier

Answer 32

hahah im singing the song ;p