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Chapter 3: Problem 8

Solve each equation. Check your result. a. \(3 x=27\) b. \(9 s=-81\) c. \(-24=-3 y\) d. \(-5 x=45\) e. \(-6 x=-18\) f. \(-x=-5\)

Short Answer

Expert verified
Answer: The values are: x = 9, s = -9, y = 8, x = -9 (for 5x = 45), and x = 3 (for -6x = -18).

Step by step solution

01

Isolate the variable x

To isolate the variable x, we need to divide both sides of the equation by the coefficient of x, which is 3: 3x/3 = 27/3.
02

Simplify the equation

After dividing both sides by 3, the equation simplifies to x = 9. So, the value of x is 9. #b. 9s = -81#
03

Isolate the variable s

To isolate the variable s, we need to divide both sides of the equation by the coefficient of s, which is 9: 9s/9 = -81/9.
04

Simplify the equation

After dividing both sides by 9, the equation simplifies to s = -9. So, the value of s is -9. #c. -24 = -3y#
05

Isolate the variable y

To isolate the variable y, we need to divide both sides of the equation by the coefficient of y, which is -3: -24/-3 = -3y/-3.
06

Simplify the equation

After dividing both sides by -3, the equation simplifies to y = 8. So, the value of y is 8. #d. -5x = 45#
07

Isolate the variable x

To isolate the variable x, we need to divide both sides of the equation by the coefficient of x, which is -5: -5x/-5 = 45/-5.
08

Simplify the equation

After dividing both sides by -5, the equation simplifies to x = -9. So, the value of x is -9. #e. -6x = -18#
09

Isolate the variable x

To isolate the variable x, we need to divide both sides of the equation by the coefficient of x, which is -6: -6x/-6 = -18/-6.
10

Simplify the equation

After dividing both sides by -6, the equation simplifies to x = 3. So, the value of x is 3. #f. -x = -5#
11

Isolate the variable x

To isolate the variable x, we need to multiply both sides of the equation by -1: -(-x) = -(-5).
12

Simplify the equation

After multiplying both sides by -1, the equation simplifies to x = 5. So, the value of x is 5.

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