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

Question

whats the answer im confused

Answer 1

To solve the equation

\[ \frac{8}{11} \left( x + \frac{4}{5} \right) = \frac{24}{55}, \]

we can start by eliminating the fraction on the left side. We can do this by multiplying both sides of the equation by \( \frac{11}{8} \):

\[ x + \frac{4}{5} = \frac{11}{8} \cdot \frac{24}{55}. \]

Next, we simplify the right side:

\[ \frac{11}{8} \cdot \frac{24}{55} = \frac{11 \cdot 24}{8 \cdot 55} = \frac{264}{440}. \]

Now, we can simplify \( \frac{264}{440} \). Both 264 and 440 can be divided by 88:

\[ \frac{264 \div 88}{440 \div 88} = \frac{3}{5}. \]

So, our equation now looks like this:

\[ x + \frac{4}{5} = \frac{3}{5}. \]

To isolate \( x \), we subtract \( \frac{4}{5} \) from both sides:

\[ x = \frac{3}{5} - \frac{4}{5}. \]

Calculating that gives:

\[ x = \frac{3 - 4}{5} = \frac{-1}{5}. \]

Thus, the solution is

\[ \boxed{-\frac{1}{5}}. \]

Answer 2

simplify 264/440

Answer 3

To simplify the fraction \(\frac{264}{440}\), we can find the greatest common divisor (GCD) of the numerator (264) and the denominator (440) and then divide both by that GCD.

1. Factorize both numbers:

   • \(264 = 2^3 \cdot 3 \cdot 11\)
   • \(440 = 2^3 \cdot 5 \cdot 11\)

2. Identify the GCD: The common factors are \(2^3\) and \(11\). Thus, the GCD is:

   \[ GCD = 2^3 \cdot 11 = 8 \cdot 11 = 88 \]

3. Divide both the numerator and the denominator by the GCD:

   \[ \frac{264 \div 88}{440 \div 88} = \frac{3}{5} \]

Therefore, the simplified form of \(\frac{264}{440}\) is

\[ \frac{3}{5}. \]