Problems $$ 8-10 $$ : Solve each equation. Show your thinking. $$ \begin{array}{ll} ext { 8. } \frac{1}{2}+x=2 & ext { 9. } \frac{2}{3} y=6\end{array} $$

Question

Problems $$ 8-10 $$ : Solve each equation. Show your thinking. $$ \begin{array}{ll}	ext { 8. } \frac{1}{2}+x=2 & 	ext { 9. } \frac{2}{3} y=6\end{array} $$

UpStudy AI · Accepted Answer

Certainly! Let's solve each equation step by step.

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### **Problem 8**

$$
\frac{1}{2} + x = 2
$$

**Solution:**

Our goal is to solve for $$ x $$.

1. **Subtract $$\frac{1}{2}$$ from both sides** to isolate $$ x $$:

$$
\frac{1}{2} + x - \frac{1}{2} = 2 - \frac{1}{2}
$$

2. **Simplify both sides**:

$$
x = \frac{4}{2} - \frac{1}{2}
$$

$$
x = \frac{3}{2}
$$

3. **Convert to decimal (optional)**:

$$
x = 1.5
$$

**Answer:** $$ x = \frac{3}{2} $$ or $$ x = 1.5 $$

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### **Problem 9**

$$
\frac{2}{3} y = 6
$$

**Solution:**

Our goal is to solve for $$ y $$.

1. **Multiply both sides by the reciprocal of $$\frac{2}{3}$$**, which is $$\frac{3}{2}$$, to isolate $$ y $$:

$$
\frac{3}{2} \times \frac{2}{3} y = 6 \times \frac{3}{2}
$$

2. **Simplify the left side** (the fractions cancel out):

$$
y = 6 \times \frac{3}{2}
$$

3. **Multiply the numbers**:

$$
y = \frac{18}{2}
$$

$$
y = 9
$$

**Answer:** $$ y = 9 $$

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Feel free to ask if you have any further questions!
**Problem 8:** $$ \frac{1}{2} + x = 2 $$ Subtract $$\frac{1}{2}$$ from both sides: $$ x = 2 - \frac{1}{2} = \frac{3}{2} \text{ or } 1.5 $$ **Problem 9:** $$ \frac{2}{3} y = 6 $$ Multiply both sides by $$\frac{3}{2}$$: $$ y = 6 \times \frac{3}{2} = 9 $$ **Answers:** - Problem 8: $$ x = \frac{3}{2} $$ or $$ 1.5 $$ - Problem 9: $$ y = 9 $$

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