Question

Solve the equation.
StartFraction x plus 5 Over 4 EndFraction equals 2 minus StartFraction x plus 3 Over 7 EndFraction

Answer 1

To solve the equation

\[
\frac{x + 5}{4} = 2 - \frac{x + 3}{7},
\]

we can start by eliminating the fractions. We will find a common denominator, which in this case is 28.

First, multiply both sides of the equation by 28:

\[
28 \cdot \frac{x + 5}{4} = 28 \cdot \left(2 - \frac{x + 3}{7}\right).
\]

This simplifies to:

\[
7(x + 5) = 56 - 4(x + 3).
\]

Now, distribute on both sides:

\[
7x + 35 = 56 - 4x - 12.
\]

Combine like terms on the right side:

\[
7x + 35 = 44 - 4x.
\]

Next, add \(4x\) to both sides to move \(x\) terms to one side:

\[
7x + 4x + 35 = 44.
\]

This simplifies to:

\[
11x + 35 = 44.
\]

Now, subtract 35 from both sides:

\[
11x = 44 - 35,
\]

which gives:

\[
11x = 9.
\]

Finally, divide both sides by 11:

\[
x = \frac{9}{11}.
\]

Thus, the solution to the equation is

\[
\boxed{\frac{9}{11}}.
\]