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Distributive Property

Directions: Identify which property justifies each step used to solve the equations below.

1.

| Equation Steps | Properties/Reasons |
|-----------------------|--------------------|
| 1. [tex]2(x-9)=-10[/tex] | 1. Given |
| 2. [tex]2x-18=-10[/tex] | 2. Distributive Property |
| 3. [tex]2x=8[/tex] | 3. Addition Property of Equality |
| 4. [tex]x=4[/tex] | 4. Division Property of Equality |

2.

| Equation Steps | Properties/Reasons |
|-----------------------------------|-------------------------------------|
| 1. [tex]\frac{m}{-3}+10=-1[/tex] | 1. Given |
| 2. [tex]\frac{m}{-3}=-11[/tex] | 2. Subtraction Property of Equality |
| 3. [tex]m=33[/tex] | 3. Multiplication Property of Equality |

3.

| Equation Steps | Properties/Reasons |
|----------------------------------|-------------------------------------|
| 1. [tex]\frac{5y-1}{2}=7[/tex] | 1. Given |
| 2. [tex]5y-1=14[/tex] | 2. Multiplication Property of Equality |
| 3. [tex]5y=15[/tex] | 3. Addition Property of Equality |
| 4. [tex]y=3[/tex] | 4. Division Property of Equality |

- Gina Wilson

Sagot :

GinnyAnsweridn
Sure! Here is the step-by-step solution for the given equations along with the properties that justify each step:

### 1. [tex]\(2(x-9)=-10\)[/tex]

1. Equation: [tex]\(2(x-9)=-10\)[/tex]
- Reason: Given

2. Equation: [tex]\(2x - 18 = -10\)[/tex]
- Reason: Distributive Property (distributing the 2 through the parentheses)

3. Equation: [tex]\(2x = 8\)[/tex]
- Reason: Addition Property of Equality (adding 18 to both sides)

4. Equation: [tex]\(x = 4\)[/tex]
- Reason: Division Property of Equality (dividing both sides by 2)

### 2. [tex]\(\frac{m}{-3}+10=-1\)[/tex]

1. Equation: [tex]\(\frac{m}{-3} + 10 = -1\)[/tex]
- Reason: Given

2. Equation: [tex]\(\frac{m}{-3} = -11\)[/tex]
- Reason: Subtraction Property of Equality (subtracting 10 from both sides)

3. Equation: [tex]\(m = 33\)[/tex]
- Reason: Multiplication Property of Equality (multiplying both sides by -3)

### 3. [tex]\(\frac{5y-1}{2}=7\)[/tex]

1. Equation: [tex]\(\frac{5y-1}{2} = 7\)[/tex]
- Reason: Given

2. Equation: [tex]\(5y - 1 = 14\)[/tex]
- Reason: Multiplication Property of Equality (multiplying both sides by 2 to eliminate the fraction)

3. Equation: [tex]\(5y = 15\)[/tex]
- Reason: Addition Property of Equality (adding 1 to both sides)

4. Equation: [tex]\(y = 3\)[/tex]
- Reason: Division Property of Equality (dividing both sides by 5)

I hope this detailed, step-by-step solution helps you understand the process of solving these equations!
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