Question

Translate each of the following into an equation and solve. Let \(x\) represent the number. a. The product of a number and \(-6\) is 54 b. \(-30\) times a number is \(-150\). c. \(-88\) is the product of a number and 8 . d. Twice a number is \(-28\).

Short answer

b. What number, when multiplied by -30, results in -150? c. What number, when multiplied by 8, results in -88? d. What number, when multiplied by 2, results in -28? a. The number that, when multiplied by -6, results in 54 is -9. b. The number that, when multiplied by -30, results in -150 is 5. c. The number that, when multiplied by 8, results in -88 is -11. d. The number that, when multiplied by 2, results in -28 is -14.

Step-by-step solution

a. The product of a number and \(-6\) is 54

Write the equation as follows: \(-6x = 54\). To solve for x, divide both sides of the equation by -6: \(x = \frac{54}{-6}\). Now, compute the value of x: \(x = -9\).

b. \(-30\) times a number is \(-150\)

Write the equation as: \(-30x = -150\). To solve for x, divide both sides of the equation by -30: \(x = \frac{-150}{-30}\). Now, compute the value of x: \(x = 5\).

c. \(-88\) is the product of a number and 8

Write the equation as: \(8x = -88\). To solve for x, divide both sides of the equation by 8: \(x = \frac{-88}{8}\). Now, compute the value of x: \(x = -11\).

d. Twice a number is \(-28\)

Write the equation as: \(2x = -28\). To solve for x, divide both sides of the equation by 2: \(x = \frac{-28}{2}\). Now, compute the value of x: \(x = -14\).