# Solve for x: 3 over 4 x + 5 over 8 = 4x?

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Solve for x: 3 over 4 x + 5 over 8 = 4x

x = __________________ Write your answer as a fraction in simplest form. Use the “/” symbol for the fraction bar.

• (3/4 x + 5) / (8) = 4x

Cross multiply:

8 (4x) = (3/4 x + 5)

32x = 3/4 x + 5

32x – 3/4x = 5

128/4 x – 3/4x = 5

125/4 x = 5

125x = 20

x = 20/125

x = 4/25

Hope this helps. 🙂

• assuming expression is

3/4x + 5/8 = 4x

is the same as

3/4x + 5/8 = (4x)/1

NOTE that our LOWEST common denominator is 8x, so multiply each fraction top and bottom until you get the denominators to have 8x.

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

2(3)/8x + x(5)/8x = 8x(4x)/8x

now drop denominators and solve using numerators

2(3) + x(5) = 8x(4x)

6 + 5x = 32x^2

32x^2 – 5x – 6 = 0

a = 32, b = -5, c = -6…..

x = (-b +/- √(b^2-4ac)) / 2a

x = (-(-5 +/- √((-5)^2 -4(32)(-6))) / 2(32)

x = (5 +/- √(25 -(-768))) / 64

x = (5 +/- √793) / 64

can’t simplify further

• I’m assuming that you have this:

(3/4x)+(5/8)=4x

And that is what I will solve.

Multiply everything by 8:

6X+5=32X

Move the 6X to the other side. When it’s on the left, its sign is + when it moves, its sign becomes –

+5=32X-6X

Solve:

5=26X

X=5/25

• 3/4x + 5/8 = 4x

– 3 1/4x = – 5/8

(4/13)13/4x = (4/13)5/8

x = 5/26.

• is the answer really 4/25

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