Home > Algebra > Multi-Step Equations with Like Terms

How do you solve #x/4 - 7/8 + 3/2x = 5/12 - 5/4x#?

Answer 1

#x=31/72#

Finding the least common multiple, or LCM, of all the numbers you have as denominators will help you eliminate the denominators first.

As an example, the LCM of

#2, 4, 8, 12#

is #24#. This means that your starting equation

#x/4 - 7/8 + (3x)/2 = 5/12 - (5x)/4#

can be expressed as

#x/4 * 6/6 - 7/8 * 3/3 + (3x)/2 * 12/12 = 5/12 * 2/2 - (5x)/4 * 6/6#

You'll get this

#(6x)/24 - 21/24 + (36x)/24 = 10/24 - (30x)/24#

You can now concentrate on the numerators.

#6x - 21 + 36x = 10 - 30x#

Gather related terms to locate

10 + 21 = 6x + 36x + 30x

#72x = 31 implies x = 31/72#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isaiah Anthony

To solve the equation ( \frac{x}{4} - \frac{7}{8} + \frac{3}{2}x = \frac{5}{12} - \frac{5}{4}x ), follow these steps:

Combine like terms on each side of the equation.
Get rid of fractions by multiplying every term by the least common denominator (LCD), which is 24 in this case.
Solve for ( x ).
Check your solution by substituting it back into the original equation to ensure it satisfies the equation.

The solution to the equation is ( x = \frac{2}{3} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.