Answered

IDNLearn.com provides a reliable platform for finding accurate and timely answers. Our community is here to provide detailed and trustworthy answers to any questions you may have.

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!
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.