Complete the missing reasons for the proof.

Given: [tex]4(x-2)=6x+18[/tex]

Prove: [tex]x=-13[/tex]

| Statements | Reasons |
|-----------------------------|----------------------------------------------|
| 1. [tex]4(x-2)=6x+18[/tex] | Given |
| 2. [tex]4x-8=6x+18[/tex] | Distributive Property |
| 3. [tex]-2x-8=18[/tex] | Subtraction Property of Equality |
| 4. [tex]-2x=26[/tex] | Addition Property of Equality |
| 5. [tex]x=-13[/tex] | Division Property of Equality |

Question

28-06-2024
Mathematics

Answered

Complete the missing reasons for the proof.

Given: [tex]4(x-2)=6x+18[/tex]

Prove: [tex]x=-13[/tex]

| Statements | Reasons |
|-----------------------------|----------------------------------------------|
| 1. [tex]4(x-2)=6x+18[/tex] | Given |
| 2. [tex]4x-8=6x+18[/tex] | Distributive Property |
| 3. [tex]-2x-8=18[/tex] | Subtraction Property of Equality |
| 4. [tex]-2x=26[/tex] | Addition Property of Equality |
| 5. [tex]x=-13[/tex] | Division Property of Equality |

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-28T16:31:54-04:00

Let's detail the step-by-step solution and complete the missing reasons for the proof.

Given equation:
[tex]\[ 4(x-2) = 6x + 18 \][/tex]

Statements and Reasons:

1. Statement: $ 4(x-2) = 6x + 18 $
- Reason: Given

2. Statement: $ 4x - 8 = 6x + 18 $
- Reason: Distributive property

3. Statement: $ 4x - 6x - 8 = 18 $
- Reason: Subtraction property of equality (subtracting $ 6x $ from both sides)

4. Statement: $ -2x - 8 = 18 $
- Reason: Combining like terms

5. Statement: $ -2x = 26 $
- Reason: Addition property of equality (adding 8 to both sides)

6. Statement: $ x = -13 $
- Reason: Division property of equality (dividing both sides by -2)

Therefore, the correct completion of the missing reasons for the proof is:
3. Subtraction property of equality
5. Division property of equality