Question

Half of the sum of a certain number and 7 is equal to one quarter of the difference of the number from 3 find the number

Answer 1

Let the certain number be \( x \).

According to the problem, half of the sum of the number and 7 is equal to one quarter of the difference of the number from 3. We can set up the equation as follows:

\[
\frac{1}{2}(x + 7) = \frac{1}{4}(3 - x)
\]

To eliminate the fractions, we can multiply both sides of the equation by 4:

\[
4 \cdot \frac{1}{2}(x + 7) = 4 \cdot \frac{1}{4}(3 - x)
\]

This simplifies to:

\[
2(x + 7) = 3 - x
\]

Next, we distribute the 2 on the left side:

\[
2x + 14 = 3 - x
\]

Now, we will add \( x \) to both sides to combine the \( x \) terms:

\[
2x + x + 14 = 3
\]

This simplifies to:

\[
3x + 14 = 3
\]

Next, we subtract 14 from both sides:

\[
3x = 3 - 14
\]

This simplifies to:

\[
3x = -11
\]

Now, we divide both sides by 3:

\[
x = -\frac{11}{3}
\]

Thus, the certain number is \( -\frac{11}{3} \).