Question 1 Complete the missing reasons for the proof. Given: 4(x - 2) = 6x + 18 Prove: x= -13 Statements Reasons 1.4(x - 2) = 6x +18 given 2. 4x8= 6x +18 distributive property 3.-2-8-18 4.-2x = 26 addition property of equality 5.x = -13 O 3. subtraction property of equality; 5. multiplication property of equality O 3. subtraction property of equality; 5. division property of equality 3. addition property of equality; 5. division property of equality O 3. addition property of equality; 5. multiplication property of equality

Looking at the problem statement, the question is asking us to determine what the missing reasons are. The information that is given to us is a step-by-step process of solving an expression for an unknown. There are also two blanks in the reasons column for steps 3 and 5 which we will need to determine.

For step #3, we can see that they subtracted 6x from both sides which means that options 3 and 4 are automatically out since they reference addition in the first part. The correct reasoning for this part would be Subtraction Property of Equality which states that we subtract the same item from both sides of the expression.

We can see this being done in the following actions

[tex]4x - 8 = 6x + 18[/tex]

[tex](4x - 6x) - 8 = (6x - 6x) + 18[/tex]

[tex](4x - 6x) - 8 = 18[/tex]

[tex]-2x - 8 = 18[/tex]

For step #5, we can see that they divided both sides by -2 which means that option 1 is out since it references the multiplication property of equality. The correct reasoning for this part would be Division Property of Equality which states that we divide both sides by the same item.

We can see this being done in the following actions

[tex]-2x = 26[/tex]

[tex]\frac{-2x}{-2} = \frac{26}{-2}[/tex]

[tex]x= \frac{26}{-2}[/tex]

[tex]x= -13[/tex]

Therefore, the option that would best fit the description that we provided during our work would be option 2 (3. subtraction property of equality; 5. division property of equality).

Esther Esther · Answer 2 · 2022-06-08T00:17:04+02:00

Answer:

b) 3. addition property of equality; 5. division property of equality.

Step-by-step explanation:

Given: 4(x - 2) = 6x + 18

Prove: x = -13

Algebraic Properties:

Addition: If a = b, then a + c = b + c
Subtraction: If a = b, then a - c = b - c
Multiplication: If a = b, then ac = bc
Division: If a = b, then a ÷ c = b ÷ c
Distributive: a(b + c) = ab + ac

Steps:

1. Given:

⟹ 4(x - 2) = 6x + 18

2. Distribute property:

4(x) + 4(-2) = 6x + 18 [distribute 4]

⟹ 4x - 8 = 6x + 18

3. Subtraction property of equality:

4x - 6x - 8 = 6x - 6x + 18 [subtract 6x from both sides]

⟹ -2x - 8 = 18

4. Addition property of equality:

-2x - 8 + 8 = 18 + 8 [add 8 to both sides]

⟹ -2x = 26

5. Division property of equality:

-2x ÷ -2 = 26 ÷ -2 [divide both sides by -2]

⟹ x = -13

In conclusion, the missing reasons are the subtraction and division properties of equality.

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