Algebra Year 9 GCSE Module

Please tell me the method to work something out like this:

3/4(x+11)-2/3(17-x)=4 (find x)

Thanks!

 

Alright, lets break this down!

First we want to get the x's alone. That's going to be hard to do though! Lets start by distributing the 3/4 and the 2/3 to all terms in their respective parenthesis:

3/4x + 33/4 - 34/3 + 2/3x = 4

Now lets add 33/4 and add 34/3 to both sides:

3/4x+2/3x = 7.05

Lets find a common denominator for that x!

9/12x + 8/12x = 7.05

17/12x = 7.05 (add the fractions)



Now multiply 7.05 by the reciprocal (12/17).

x = 13.2

Check my work, it's a million degrees here. I'm pretty sure it's correct, but if you follow the steps I did and get a different answer let me know.

 

I would multiply the whole thing by 12 first, and then distribute. It makes it easier, in my opinion.

 

i would type whole thing into my calculator and hit solve x button. ( im too lazy to do now haha)

 

12 is the lowest common denominator for all of the numbers, true. The problem is though, in other situations you'll have to find another lowest common denominator that might not be that easy to spot (especially if you're dealing with 16 fractions from a Lagrangian equation or 10 fractions from a Riemann tensor).

 

3/4(x+11)-2/3(17-x)=4 (find x)

3/4x + 33/4 -34/3 +2/3x = 4

multiply by 12

9x + 99 - 136x + 8x = 48

17x = 85

x = 5

Plug this back in and

3/4(5+11)-2/3(17-5)=4 (find x)

3/4(16) -2/3(12) = 4

12 -8 = 4