how would solve this math question 5/8x - 6 3/8x = 1 1/2
To solve the equation 5/8x - 6 3/8x = 1 1/2, we need to simplify and combine like terms. Let's break it down step by step:
Step 1: Convert mixed numbers to improper fractions.
6 3/8 can be expressed as (6 * 8 + 3)/8 = 51/8.
1 1/2 can be expressed as (1 * 2 + 1)/2 = 3/2.
The equation becomes:
5/8x - 51/8x = 3/2
Step 2: Find the common denominator.
The common denominator of 8 and 2 is 8.
The equation becomes:
(5/8 - 51/8)x = 3/2
Step 3: Combine like terms.
5/8 - 51/8 = -46/8 = -23/4
The equation simplifies to:
(-23/4)x = 3/2
Step 4: Isolate the variable.
Multiply both sides of the equation by the reciprocal of -23/4, which is -4/23:
((-23/4)x) * (-4/23) = (3/2) * (-4/23)
The equation becomes:
x = (-12/46) = -6/23
So the solution to the equation 5/8x - 6 3/8x = 1 1/2 is x = -6/23.