11. Construct two concentric circles that have a radius of 3 cm and a radius of 4 cm . member r problems $$ 12-15 $$, solve for $$ x $$. $$ x+2 \frac{4}{5}=66 $$ 13. $$ -\frac{7}{5}+x=7 \frac{1}{5} $$ 14. $$ x+\left(-9 \frac{1}{2}\right)=-7 $$ 15. $$ -25 \frac{2}{3}=x-3 \frac{1}{3} $$

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Sure, let's tackle each of these problems step by step.

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### **11. Construct Two Concentric Circles with Radii of 3 cm and 4 cm**

**Concentric circles** are circles that share the same center but have different radii.

**Materials Needed:**
- Compass
- Pencil
- Ruler
- Paper

**Steps:**

1. **Draw the First Circle:**
   - Place the compass point on the paper where you want the center of the circles to be; label this point **O**.
   - Adjust the compass so that the distance between the point and pencil is **3 cm**.
   - Draw the first circle centered at **O** with a radius of **3 cm**.

2. **Draw the Second Circle:**
   - Without changing the position of point **O**, adjust the compass to have a distance of **4 cm** between the point and pencil.
   - Draw the second circle centered at **O** with a radius of **4 cm**.

**Result:** You will have two circles that share the same center **O**, with one having a radius of **3 cm** and the other **4 cm**.

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### **Solving for $$ x $$ in Problems 12-15**

Let's solve each equation step by step.

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#### **12. $$ x + 2 \frac{4}{5} = 66 $$**

**Step 1:** Convert the mixed number to an improper fraction.
$$ 2 \frac{4}{5} = \frac{14}{5} $$

**Step 2:** Rewrite the equation.
$$ x + \frac{14}{5} = 66 $$

**Step 3:** Subtract $$\frac{14}{5}$$ from both sides to isolate $$ x $$.
$$ x = 66 - \frac{14}{5} $$

**Step 4:** Convert 66 to a fraction with denominator 5.
$$ 66 = \frac{330}{5} $$

**Step 5:** Perform the subtraction.
$$ x = \frac{330}{5} - \frac{14}{5} = \frac{316}{5} $$

**Step 6:** Convert back to a mixed number if desired.
$$ x = 63 \frac{1}{5} $$

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#### **13. $$ -\frac{7}{5} + x = 7 \frac{1}{5} $$**

**Step 1:** Convert the mixed number to an improper fraction.
$$ 7 \frac{1}{5} = \frac{36}{5} $$

**Step 2:** Rewrite the equation.
$$ -\frac{7}{5} + x = \frac{36}{5} $$

**Step 3:** Add $$\frac{7}{5}$$ to both sides to isolate $$ x $$.
$$ x = \frac{36}{5} + \frac{7}{5} $$

**Step 4:** Perform the addition.
$$ x = \frac{43}{5} $$

**Step 5:** Convert back to a mixed number if desired.
$$ x = 8 \frac{3}{5} $$

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#### **14. $$ x + \left(-9 \frac{1}{2}\right) = -7 $$**

**Step 1:** Rewrite the equation.
$$ x - 9 \frac{1}{2} = -7 $$

**Step 2:** Add $$9 \frac{1}{2}$$ to both sides to isolate $$ x $$.
$$ x = -7 + 9 \frac{1}{2} $$

**Step 3:** Convert mixed numbers to improper fractions.
$$ -7 = -\frac{14}{2} $$
$$ 9 \frac{1}{2} = \frac{19}{2} $$

**Step 4:** Perform the addition.
$$ x = -\frac{14}{2} + \frac{19}{2} = \frac{5}{2} $$

**Step 5:** Convert back to a mixed number if desired.
$$ x = 2 \frac{1}{2} $$

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#### **15. $$ -25 \frac{2}{3} = x - 3 \frac{1}{3} $$**

**Step 1:** Convert all mixed numbers to improper fractions.
$$ -25 \frac{2}{3} = -\frac{77}{3} $$
$$ 3 \frac{1}{3} = \frac{10}{3} $$

**Step 2:** Rewrite the equation.
$$ -\frac{77}{3} = x - \frac{10}{3} $$

**Step 3:** Add $$\frac{10}{3}$$ to both sides to isolate $$ x $$.
$$ x = -\frac{77}{3} + \frac{10}{3} $$

**Step 4:** Perform the addition.
$$ x = -\frac{67}{3} $$

**Step 5:** Convert back to a mixed number if desired.
$$ x = -22 \frac{1}{3} $$

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### **Summary of Solutions:**

1. **Problem 12:** $$ x = 63 \frac{1}{5} $$ or $$ x = 63.2 $$
2. **Problem 13:** $$ x = 8 \frac{3}{5} $$ or $$ x = 8.6 $$
3. **Problem 14:** $$ x = 2 \frac{1}{2} $$ or $$ x = 2.5 $$
4. **Problem 15:** $$ x = -22 \frac{1}{3} $$ or $$ x = -22.333... $$

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Feel free to ask if you need further clarification on any of these problems!
Solutions for the equations are: 12. $$ x = 63 \frac{1}{5} $$ 13. $$ x = 8 \frac{3}{5} $$ 14. $$ x = 2 \frac{1}{2} $$ 15. $$ x = -22 \frac{1}{3} $$

11. Construct two concentric circles that have a radius of 3 cm and a radius of 4 cm . member r problems \( 12-15 \), solve for \( x \). \( x+2 \frac{4}{5}=66 \) 13. \( -\frac{7}{5}+x=7 \frac{1}{5} \) 14. \( x+\left(-9 \frac{1}{2}\right)=-7 \) 15. \( -25 \frac{2}{3}=x-3 \frac{1}{3} \)

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