Question

1 1/3 * (1/3- x) = 8/27

Answer 1

Ответ:

$x=\frac{1}{9}.$

Пошаговое объяснение:

$1\frac{1}{3}(\frac{1}{3}-x)=\frac{8}{27}\\\frac{4}{3}(\frac{1}{3}-x)=\frac{8}{27}\\\frac{1}{3}-x=\frac{8}{27}:\frac{4}{3}=\frac{8}{27}*\frac{3}{4}=\frac{2}{9}\\x=\frac{1}{3}-\frac{2}{9}=\frac{1*3-2}{9}=\frac{1}{9}$

Answer 2

To solve the equation 1 1/3 * (1/3 - x) = 8/27, we can follow these steps:

Step 1: Convert the mixed number 1 1/3 to an improper fraction. 1 1/3 is equivalent to (3 * 1 + 1) / 3 = 4/3.

Step 2: Rewrite the equation with the fractions. 4/3 * (1/3 - x) = 8/27.

Step 3: Distribute the 4/3 to the terms inside the parentheses. (4/3) * (1/3) - (4/3) * x = 8/27.

Step 4: Simplify the expressions on both sides. 4/9 - (4/3) * x = 8/27.

Step 5: Multiply (4/3) by x. 4/9 - (4/3) * x = 8/27 can be rewritten as - (4/3) * x + 4/9 = 8/27.

Step 6: Move the constant term to the other side. -(4/3) * x = 8/27 - 4/9.

Step 7: Find a common denominator for the fractions on the right side. The common denominator for 27 and 9 is 27. Rewriting the equation: -(4/3) * x = (8/27) - (4/9) can be simplified to -(4/3) * x = (8 - 12)/27.

Step 8: Simplify the expression on the right side. -(4/3) * x = -4/27.

Step 9: Multiply both sides by -3/4 to isolate x. x = (-4/27) * (-3/4).

Step 10: Simplify the expression on the right side. x = 12/108.

Step 11: Simplify the fraction. x = 1/9.

Therefore, the solution to the equation 1 1/3 * (1/3 - x) = 8/27 is x = 1/9.