Okay….

3 ………….2

—– = ————

(x-1)…….(4x+5)

cross multiply…. ** It may help you to draw a light dotted line from the “3” to the (4x + 5)…. THEN, draw a light dotted line from the (x-1) to the “2” ** Do you see the “dotted X” that you drew? That’s what we mean by “cross-multiplying”… this “math trick” works when you have two fractions that are equal to each other….

Sooo…. if you “cross-multiply” (that is, “denominator of left fraction TIMES numerator of 2nd fraction” EQUALS “numerator of 1st fraction TIMES denominator of 2nd fraction”)… you will get this…

(x-1)(2) = (3)(4x+5) ** Do you see what I just did??? **

Now it’s just math…

(x)(2) + (-1)(2) = (3)(4x) + (3)(+5)

2x – 2 = 12x +15

subtract “2x” from both sides… like this…

(2x – 2) -2x = (12x + 15) – 2x

combine “like” terms…. and you get…

-2 = 10x + 15

now subtract “15” from both sides… like this…

-2 -15 = (10x +15) -15

combine “like” terms like before and you get…

-17 = 10x which is the same as 10x = -17

divide both sides by 10… like this…

10x / 10 = -17/10

the 10’s on the left side cancel each other out… leaving you with…

x = -17/10 or -1.7

Plug x = -1.7 into the original equation to check… like this… (Note: if the two fractions don’t equal each other when you plug in x = -1.7, then that means that you made a mistake somewhere with you math…)

3 ………….2

—– = ————

(x-1)…….(4x+5)

So… when x = -1.7, then the above becomes….

…..3…………..2

———— = ————

(-1.7-1)…….4(-1.7)+5

3……………. 2

——- = —————-

(-2.7)…….. -6.8 + 5

…..3 …………. 2

——— = —————

(-2.7) ……… -1.8

You have a calculator, right?

3 / -2.7 = -1.11111111……

2 / -1.8 = -1.11111111…..

Both sides equal -1.11111…..

So that means that that “x = -1.7” that you found before is the solution/answer to this math problem

Hope this helps and you understand how to do this now…

Earthdrivenforce gave a good answer. I just want to say that if you are struggling with basic concepts in math (like cross-multiplying), I urge you to see your math teacher, or parent, or science teacher, or someone who really understands what to do and WHY and have them re-teach you. I find that students who struggle, especially in math, just missed a piece somewhere along the way, and after that, things fell apart. I bet with a little bit of extra help that targets the concept you don’t get (and not a specific HW problem) you will be back on your feet. SO many people feel they are “math idiots” because they don’t get one thing. I think this is because math you learn one day depends on math you learned the day before and if you lose the train of thought it can seem overwhelming to get back on track. Go get help from a sympathetic teacher! You’ll be glad you did.

cross multiply

x=(-17over 10)