Solve the equation. $$ \frac{x+1}{4}+\frac{x+1}{7}=2 $$

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UpStudy AI · Accepted Answer

1. Start with the equation:
   $$
   \frac{x+1}{4}+\frac{x+1}{7}=2
   $$

2. Notice that both fractions have the same numerator $$(x+1)$$. Factor it out by writing the sum with a common denominator:
   $$
   \frac{x+1}{4}+\frac{x+1}{7} = (x+1) \left(\frac{1}{4}+\frac{1}{7}\right)
   $$

3. Find the sum inside the parentheses. First, compute the sum by finding a common denominator:
   $$
   \frac{1}{4}+\frac{1}{7} = \frac{7}{28}+\frac{4}{28}=\frac{11}{28}
   $$

4. Substitute back to get:
   $$
   (x+1)\frac{11}{28}=2
   $$

5. To solve for $$ x+1 $$, multiply both sides of the equation by the reciprocal of $$\frac{11}{28}$$:
   $$
   x+1 = 2 \times \frac{28}{11} = \frac{56}{11}
   $$

6. Finally, subtract 1 from both sides to solve for $$ x $$:
   $$
   x = \frac{56}{11} - 1
   $$
   Express $$ 1 $$ as $$\frac{11}{11}$$ so:
   $$
   x = \frac{56}{11} - \frac{11}{11} = \frac{45}{11}
   $$

Thus, the solution is:
$$
x= \frac{45}{11}
$$
$$ x = \frac{45}{11} $$

Solve the equation.

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