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How do you solve #5/7x-3/14=-3/8x+3/4#?

Answer 1

#x=54/61#

The easiest way to solve this is to get rid of the denominators first. The least common multiple of 7, 14, 8 and 4 would be #7*8=4*14=56#.

Therefore, multiply both sides with 56=4*14: #(5/7x-3/14)*4*14=(-3/8x+3/4)*8*7#

Simplifying we get: #5*8x-3*4=-3*7x+3*14# or: #40x-12=-21x+42#

Adding #21x+12# to both sides to get the x terms to the left and the constants to the right, we get: #40x+21x= 42+12# #61x=54# Dividing on 61 on both sides we get #x=54/61#

As #61# is a prime number, we cannot simplify this more .

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Answer 2

Ethan Adkins

To solve the equation ( \frac{5}{7}x - \frac{3}{14} = -\frac{3}{8}x + \frac{3}{4} ), follow these steps:

To eliminate the fractions, multiply every term in the equation by the least common denominator, which is ( 56 ).
After multiplying, the equation becomes ( 40x - 6 = -21x + 42 ).
Add ( 21x ) to both sides: ( 61x - 6 = 42 ).
Add ( 6 ) to both sides: ( 61x = 48 ).
Divide both sides by ( 61 ): ( x = \frac{48}{61} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.