Solve for x and the equation 8/11(x+4/5)=24/55

Answer 1

To solve this equation for x, we'll follow these steps:

Step 1: Distribute 8/11 to the terms inside the parentheses.
(8/11) * (x + 4/5) = 24/55

This simplifies to:
8/11x + 8/11 * 4/5 = 24/55

Step 2: Simplify the expression 8/11 * 4/5.
8/11 * 4/5 = 32/55

So the equation becomes:
8/11x + 32/55 = 24/55

Step 3: Move 32/55 to the other side by subtracting it from both sides of the equation.
8/11x = 24/55 - 32/55

This simplifies to:
8/11x = -8/55

Step 4: Solve for x by multiplying both sides of the equation by the reciprocal of 8/11, which is 11/8.
(11/8)(8/11x) = (11/8)(-8/55)

The x terms on the left side cancel out, leaving us with:
x = -88/440

Step 5: Simplify the fraction -88/440.
x = -1/5

So the solution to the equation 8/11(x + 4/5) = 24/55 is x = -1/5.