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solve and show working out of the following

Let's solve each of these linear equations step-by-step and check the answers by substitution.

### Part (a)
\[ y - 7.3 = 5.5 \]

1. Add 7.3 to both sides:
\[ y = 5.5 + 7.3 \]
\[ y = 12.8 \]

**Check by Substitution:**
\[ 12.8 - 7.3 = 5.5 \]
\[ 5.5 = 5.5 \]
The solution is correct.

### Part (b)
\[ 6y = 14 \]

1. Divide both sides by 6:
\[ y = \frac{14}{6} \]
\[ y = \frac{7}{3} \]
\[ y \approx 2.33 \]

**Check by Substitution:**
\[ 6 \cdot \frac{7}{3} = 14 \]
\[ 14 = 14 \]
The solution is correct.

### Part (c)
\[ 0.9y = -0.05 \]

1. Divide both sides by 0.9:
\[ y = \frac{-0.05}{0.9} \]
\[ y \approx -0.0556 \]

**Check by Substitution:**
\[ 0.9 \cdot -0.0556 \approx -0.05 \]
\[ -0.05 \approx -0.05 \]
The solution is correct.

### Part (d)
\[ \frac{y}{5} = 4.3 \]

1. Multiply both sides by 5:
\[ y = 4.3 \cdot 5 \]
\[ y = 21.5 \]

**Check by Substitution:**
\[ \frac{21.5}{5} = 4.3 \]
\[ 4.3 = 4.3 \]
The solution is correct.

### Part (e)
\[ \frac{y}{7.5} = 23 \]

1. Multiply both sides by 7.5:
\[ y = 23 \cdot 7.5 \]
\[ y = 172.5 \]

**Check by Substitution:**
\[ \frac{172.5}{7.5} = 23 \]
\[ 23 = 23 \]
The solution is correct.

### Part (f)
\[ \frac{y}{8} = -1.04 \]

1. Multiply both sides by 8:
\[ y = -1.04 \cdot 8 \]
\[ y = -8.32 \]

**Check by Substitution:**
\[ \frac{-8.32}{8} = -1.04 \]
\[ -1.04 = -1.04 \]
The solution is correct.

Would you like more details on any of these steps or have any questions?

Here are 5 numbered questions you might want to ask:

1. Can you explain the process of checking solutions by substitution?
2. How do you handle linear equations with decimals?
3. What are the common mistakes to avoid when solving equations involving fractions?
4. Can you provide more examples of solving linear equations?
5. How do you solve linear equations with variables on both sides?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy the equation. This helps catch any errors made during the solving process.

Learn how to solve linear equations step-by-step with detailed working out for various types of equations. This problem covers solving equations with integers, decimals, and fractions using methods like substitution and multiplication/division. Suitable for high school students.

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