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

1 answer

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 \( -\frac{11}{3} \).