consider the following equations

Question

2/3x - 5 = 27

determine the best two steps to solve the equation.

identify the solution

Answer 1

To solve the equation \( \frac{2}{3}x - 5 = 27 \), we can follow these two steps:

Step 1: Add 5 to both sides

First, isolate the term containing \( x \) by adding 5 to both sides of the equation: \[ \frac{2}{3}x - 5 + 5 = 27 + 5 \] This simplifies to: \[ \frac{2}{3}x = 32 \]

Step 2: Multiply both sides by \( \frac{3}{2} \)

Next, to solve for \( x \), multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \): \[ x = 32 \times \frac{3}{2} \] Calculating the right side gives: \[ x = 48 \]

Solution

The solution to the equation \( \frac{2}{3}x - 5 = 27 \) is \( x = 48 \).

Answer 2

consider the equation

-27x - 5 = -21
determine the best two steps to solve the equation

identify the solution

Answer 3

To solve the equation \( -27x - 5 = -21 \), we can follow these two steps:

Step 1: Add 5 to both sides

First, isolate the term containing \( x \) by adding 5 to both sides of the equation: \[ -27x - 5 + 5 = -21 + 5 \] This simplifies to: \[ -27x = -16 \]

Step 2: Divide both sides by -27

Next, divide both sides by -27 to solve for \( x \): \[ x = \frac{-16}{-27} \] This simplifies to: \[ x = \frac{16}{27} \]

Solution

The solution to the equation \( -27x - 5 = -21 \) is \( x = \frac{16}{27} \).