Question

Solve the equation.
one half x plus 2 equals StartFraction 4 x plus 7 Over 4 EndFraction
1
2x+2=
4x+7
4

Answer 1

To solve the equation

\[
\frac{1}{2}x + 2 = \frac{4x + 7}{4},
\]

let's first eliminate the fraction by multiplying both sides of the equation by 4:

\[
4\left(\frac{1}{2}x + 2\right) = 4\left(\frac{4x + 7}{4}\right).
\]

This simplifies to:

\[
2x + 8 = 4x + 7.
\]

Next, we will isolate \(x\). Start by subtracting \(2x\) from both sides:

\[
8 = 4x - 2x + 7,
\]

which simplifies to:

\[
8 = 2x + 7.
\]

Now, subtract 7 from both sides:

\[
8 - 7 = 2x,
\]

which gives us:

\[
1 = 2x.
\]

Finally, divide both sides by 2:

\[
x = \frac{1}{2}.
\]

Thus, the solution to the equation is

\[
\boxed{\frac{1}{2}}.
\]