Solve the equation. $$ \frac{x+2}{5}+\frac{x+2}{8}=1 $$

Question

UpStudy AI · Accepted Answer

1. Multiply both sides of the equation by the least common multiple of $$5$$ and $$8$$, which is $$40$$, to eliminate the denominators:
   $$
   40 \cdot \left(\frac{x+2}{5} + \frac{x+2}{8}\right) = 40\cdot1.
   $$

2. Distribute $$40$$ to each fraction:
   $$
   \frac{40(x+2)}{5} + \frac{40(x+2)}{8} = 40.
   $$

3. Simplify each term:
   $$
   8(x+2) + 5(x+2) = 40.
   $$

4. Combine like terms:
   $$
   \left(8 + 5\right)(x+2) = 40,
   $$
   $$
   13(x+2) = 40.
   $$

5. Isolate $$x+2$$ by dividing both sides by $$13$$:
   $$
   x+2 = \frac{40}{13}.
   $$

6. Solve for $$x$$ by subtracting $$2$$ from both sides:
   $$
   x = \frac{40}{13} - 2.
   $$

7. Express $$2$$ with a common denominator:
   $$
   x = \frac{40}{13} - \frac{26}{13} = \frac{14}{13}.
   $$

Thus, the solution of the equation is:
$$
x = \frac{14}{13}.
$$
$$ x = \frac{14}{13} $$

Solve the equation.

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