Looking at the problem statement, we are told to complete the missing reasons that are not provided in the table that was given. On steps 3 and 5 we can see that the reasons column has been left blank for us to determine.
Now that we know what we must accomplish in this problem, let us understand the different algebraic properties of equality.
- Addition Property of Equality ⇒ If a = b, then a + c = b + c
- Subtraction Property of Equality ⇒ If a = b, then a - c = b - c
- Multiplication Property of Equality ⇒ If a = b, then ac = bc
- Division Property of Equality ⇒ If a = b, then a ÷ c = b ÷ c
We now understand the different algebraic properties of equalities that can be used in the problem that we have. Looking at the first blank, we can see that during that step we subtracted 6x from both sides which means that we used the Subtraction Property of Equality.
Subtract 6x from both sides
- [tex]4x - 8 = 6x + 18[/tex]
- [tex]4x - 6x - 8 = 6x - 6x + 18[/tex]
- [tex]4x - 6x - 8 = 18[/tex]
Looking at the second blank now, we can see that during that step we divided both sides by -2 which means that we used the Multiplication Property of Equality.
Divide both sides by -2
- [tex]\frac{-2x}{-2} = \frac{26}{-2}[/tex]
- [tex]x = \frac{26}{-2}[/tex]
Therefore, the best option that would fit our description would be option C, 3. subtraction property of equality; 5. multiplication property of equality.
Learn more about the other properties:
brainly.com/question/27865450
