solve for x in the equation:
8/11 (x + 4/5) = 24/55
(Show your work plz!)
To solve for x in the equation 8/11 (x + 4/5) = 24/55, follow the steps below:
1. Distribute 8/11 to the terms inside the parenthesis:
(8/11) * x + (8/11) * (4/5) = 24/55
2. Simplify the expression inside the parenthesis by multiplying the numerators and the denominators separately:
8x/11 + (32/55) = 24/55
3. Combine the fractions on the left side of the equation:
8x/11 + 32/55 = 24/55
4. To eliminate the fractions, multiply every term in the equation by the least common denominator (LCD) of 11 and 55, which is 55:
55 * (8x/11) + 55 * (32/55) = 55 * (24/55)
Simplifying this, we get:
440x/11 + 32 = 24
5. Subtract 32 from both sides of the equation:
440x/11 = 24 - 32
440x/11 = -8
6. Multiply both sides of the equation by the reciprocal of 440/11, which is 11/440:
(11/440) * (440x/11) = (11/440) * -8
Simplifying this, we get:
x = -8 * 11/440
x = -88/440
x = -1/5
Therefore, the solution to the equation 8/11 (x + 4/5) = 24/55 is x = -1/5.