Question

Please help solve!
(x+1)/3 + (x+2)/7 = 5

Answer 1

\[\frac{x+1}{3}+\frac{x+2}{7}=5\]

Answer 2

you need to get common denominators

Answer 3

how would i do that? I'm rusty :p

Answer 4

You need to find what number 3 and 7 both go into evenly

Answer 5

I know its 21

Answer 6

but what is that trick where you multiply the bottom by something and add it to the top? thats what i can't remember

Answer 7

So lets just say for the sake of anything ...that number is 21 (because it is :P)

We need to multiply the whole first term by 7/7 (to make the denominator 21) and multiply the whole second term by 3/3 (to make that denominator 21 as well)

\[\large \frac{7}{7}(\frac{x + 1}{3}) + \frac{3}{3}(\frac{x + 2}{7}) = 5\]
\[\large \frac{7(x + 1)}{21} + \frac{3(x + 2)}{21} = 5\]
Put both the terms over that common 21
\[\large \frac{7(x + 1) + 3(x + 2)}{21} = 5\]
Multiply both sides by 21
\[\large 7(x + 1) + 3(x + 2) = 105\]
Distribute as needed
\[\large 7x + 7 + 3x + 6 = 105\]
Combine like terms
\[\large 10x + 13 = 105\]
Subtract 13 from both sides of this equation
\[\large 10x = 92\]
Divide both sides by 10
\[\large x = 9.2\]

Now lets check it

\[\large \frac{x + 1}{3} + \frac{x + 2}{7} = 5\]
becomes
\[\large \frac{9.2 + 1}{3} + \frac{9.2 + 2}{7} = 5\]
\[\large \frac{10.2}{3} + \frac{11.2}{7} = 5\]
\[\large 3.4 + 1.6 = 5\]
\[\large 5 = 5 \color \red{\checkmark} \]

Answer 8

That trick you're talking about would be when you multiply both the top AND bottom by the number needed to make the common denominator :)

Answer 9

ohhh thank you SO much!! :)