Problems 8-10: Solve each equation. Show your thinking. $$ \begin{array}{ll} ext { 8. } \frac{1}{2}+x=2 & ext { 9. } \frac{2}{3} y=6\end{array} $$ 10. $$ 3=\frac{1}{4} b $$

Question

Problems 8-10: Solve each equation. Show your thinking. $$ \begin{array}{ll}	ext { 8. } \frac{1}{2}+x=2 & 	ext { 9. } \frac{2}{3} y=6\end{array} $$ 10. $$ 3=\frac{1}{4} b $$

UpStudy AI · Accepted Answer

Sure, let's solve each of the equations step by step.

---

### **Problem 8:**  
$$
\frac{1}{2} + x = 2
$$

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

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

**Step 2:**  
Convert $$2$$ to a fraction with the same denominator to subtract easily.

$$
2 = \frac{4}{2}
$$

$$
x = \frac{4}{2} - \frac{1}{2} = \frac{3}{2}
$$

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

---

### **Problem 9:**  
$$
\frac{2}{3} y = 6
$$

**Step 1:**  
To solve for $$y$$, multiply both sides of the equation by the reciprocal of $$\frac{2}{3}$$, which is $$\frac{3}{2}$$.

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

**Step 2:**  
Multiply the numbers.

$$
y = \frac{18}{2} = 9
$$

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

---

### **Problem 10:**  
$$
3 = \frac{1}{4} b
$$

**Step 1:**  
To solve for $$b$$, multiply both sides of the equation by $$4$$, which is the reciprocal of $$\frac{1}{4}$$.

$$
3 \times 4 = b
$$

**Step 2:**  
Perform the multiplication.

$$
12 = b
$$

**Final Answer:**  
$$
b = 12
$$

---

If you have any more questions or need further clarification, feel free to ask!
**Problem 8:** $$ x = \frac{3}{2} \quad \text{or} \quad x = 1.5 $$ **Problem 9:** $$ y = 9 $$ **Problem 10:** $$ b = 12 $$

Problems 8-10: Solve each equation. Show your thinking.

10.

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Problem 8:

Problem 9:

Problem 10:

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Problems 8-10: Solve each equation. Show your thinking. 10.