Question

For the following linear equations, determine which inverse operation allows you to determine the solution of the equation. In your final answer, also include the solution to each equation.
1. n/5=-0.3
2. -2n=4 1/3

Answer 1

To solve the given linear equations, we need to determine the inverse operations that will allow us to isolate the variable \( n \), and then find the solution for each equation.

### 1. Equation: \( \frac{n}{5} = -0.3 \)

**Inverse Operation:**
To isolate \( n \), we multiply both sides of the equation by 5 (the inverse of dividing by 5).

**Solution:**
\[
n = -0.3 \times 5
\]
\[
n = -1.5
\]

### 2. Equation: \( -2n = 4 \frac{1}{3} \)

First, convert \( 4 \frac{1}{3} \) to an improper fraction:
\[
4 \frac{1}{3} = \frac{13}{3}
\]

**Inverse Operation:**
To isolate \( n \), we can first divide both sides by -2 (the inverse operation of multiplying by -2).

**Solution:**
\[
n = \frac{\frac{13}{3}}{-2}
\]
This simplifies to:
\[
n = \frac{13}{3} \times \frac{-1}{2} = \frac{-13}{6}
\]

**Final Answers:**
1. \( n = -1.5 \) (found by multiplying both sides by 5).
2. \( n = -\frac{13}{6} \) (found by dividing both sides by -2).

Answer 2

can you make it less advanced

Answer 3

Of course! Let’s break it down into simpler steps to solve each equation and find the answer.

### 1. Equation: \( \frac{n}{5} = -0.3 \)

**Step to Solve:**
- To find \( n \), we need to get rid of the division by 5. We do this by multiplying both sides by 5.

**Calculation:**
\[
n = -0.3 \times 5
\]
\[
n = -1.5
\]

### Solution:
- The answer for the first equation is **\( n = -1.5 \)**.

---

### 2. Equation: \( -2n = 4 \frac{1}{3} \)

First, let’s change \( 4 \frac{1}{3} \) into a format that’s easier to work with:
- \( 4 \frac{1}{3} \) can be written as \( \frac{13}{3} \).

**Step to Solve:**
- To find \( n \), we need to get rid of the \( -2 \). We can do this by dividing both sides by -2.

**Calculation:**
\[
n = \frac{\frac{13}{3}}{-2}
\]
- When dividing a fraction by a number, we flip the number (which is the same as multiplying by the reciprocal):

**Continue Calculation:**
\[
n = \frac{13}{3} \div -2 = \frac{13}{3} \times \frac{-1}{2}
\]
\[
n = \frac{-13}{6}
\]

### Solution:
- The answer for the second equation is **\( n = -\frac{13}{6} \)**.

---

### Final Answers:
1. For \( \frac{n}{5} = -0.3 \), the solution is **\( n = -1.5 \)**.
2. For \( -2n = 4 \frac{1}{3} \), the solution is **\( n = -\frac{13}{6} \)**.

Answer 4

can you use less words

Answer 5

Sure! Here’s a more concise version:

### 1. Equation: \( \frac{n}{5} = -0.3 \)

**Solve:**
- Multiply both sides by 5:
\[
n = -0.3 \times 5 \\
n = -1.5
\]

### Solution:
- **\( n = -1.5 \)**

---

### 2. Equation: \( -2n = 4 \frac{1}{3} \)

- Convert to improper fraction: \( 4 \frac{1}{3} = \frac{13}{3} \)

**Solve:**
- Divide both sides by -2:
\[
n = \frac{\frac{13}{3}}{-2} \\
n = \frac{-13}{6}
\]

### Solution:
- **\( n = -\frac{13}{6} \)**