Answer :
Certainly! Let's break down the equation [tex]\(\frac{2}{3}y + 15 = 9\)[/tex] step-by-step to solve for [tex]\(y\)[/tex].
Here are the steps and justifications:
| Steps | Justifications |
|-----------------------------------------|-----------------------------------------|
| [tex]\(\frac{2}{3}y + 15 = 9\)[/tex] | Given |
| [tex]\(\frac{2}{3}y + 15 - 15 = 9 - 15\)[/tex] | Subtraction property of equality |
| [tex]\(\frac{2}{3}y = -6\)[/tex] | Simplification |
| [tex]\(\frac{2}{3}y \frac{3}{2} = -6 \frac{3}{2}\)[/tex] | Multiplication property of equality |
| [tex]\(y = -9\)[/tex] | Simplification |
So, the fully populated table with the correct steps and justifications is:
| Steps | Justifications |
|-----------------------------------------|-----------------------------------------|
| [tex]\(\frac{2}{3}y + 15 = 9\)[/tex] | Given |
| [tex]\(\frac{2}{3}y + 15 - 15 = 9 - 15\)[/tex] | Subtraction property of equality |
| [tex]\(\frac{2}{3}y = -6\)[/tex] | Simplification |
| [tex]\(\frac{2}{3}y \frac{3}{2} = -6 \frac{3}{2}\)[/tex] | Multiplication property of equality |
| [tex]\(y = -9\)[/tex] | Simplification |
Here are the steps and justifications:
| Steps | Justifications |
|-----------------------------------------|-----------------------------------------|
| [tex]\(\frac{2}{3}y + 15 = 9\)[/tex] | Given |
| [tex]\(\frac{2}{3}y + 15 - 15 = 9 - 15\)[/tex] | Subtraction property of equality |
| [tex]\(\frac{2}{3}y = -6\)[/tex] | Simplification |
| [tex]\(\frac{2}{3}y \frac{3}{2} = -6 \frac{3}{2}\)[/tex] | Multiplication property of equality |
| [tex]\(y = -9\)[/tex] | Simplification |
So, the fully populated table with the correct steps and justifications is:
| Steps | Justifications |
|-----------------------------------------|-----------------------------------------|
| [tex]\(\frac{2}{3}y + 15 = 9\)[/tex] | Given |
| [tex]\(\frac{2}{3}y + 15 - 15 = 9 - 15\)[/tex] | Subtraction property of equality |
| [tex]\(\frac{2}{3}y = -6\)[/tex] | Simplification |
| [tex]\(\frac{2}{3}y \frac{3}{2} = -6 \frac{3}{2}\)[/tex] | Multiplication property of equality |
| [tex]\(y = -9\)[/tex] | Simplification |