Questions: The sum of a number times 8 and 12 is equal to the difference between the number and 9

Solution Steps

Let the unknown number be \( x \).

The sum of the number times 8 and 12 is written as \( 8x + 12 \). The difference between the number and 9 is written as \( x - 9 \). According to the problem, these two expressions are equal: \[ 8x + 12 = x - 9 \]

Subtract \( x \) from both sides: \[ 8x - x + 12 = -9 \] \[ 7x + 12 = -9 \]

Subtract 12 from both sides: \[ 7x = -9 - 12 \] \[ 7x = -21 \]

Divide both sides by 7: \[ x = \frac{-21}{7} \] \[ x = -3 \]

Final Answer