11) 3 (2x + 7) - 4 = 53 - 3x is the given
Then, we use distributive property and get:
6x + 21 - 4 = 53 - 3x
Next, we combine like terms
6x + 17 = 53 - 3x
Then, we use the addition property of equality to add 3x to both sides.
9x + 17 = 53
We then use the subtraction property of equality to subtract 17 from both sides.
9x = 36
Finally, we use the division property of equality to divide 36 by 9, which isolates x.
x = 4
So, (In order) you have the: Given, Distributive Property, Combine Like Terms, Addition Property of Equality, Subtraction Property of Equality, and Division Property of Equality.
12) Please Note: This is an inequality problem. Which means we do not use the properties of equality. We'd use the properties of order. Properties of order are specific to inequalities, as the properties of equality are specific to the equations. They do not cross. As for your paper, I'm not sure why it says to use the properties of equality. I will be using the properties of order.
-7 (3 + 8x) + 5x ≤ 1 - 62x is the given
-21 - 56x + 5x ≤ 1 - 62x is distributive property
We then combine like terms
-21 - 51x ≤ 1 - 62x
Next, we use subtraction property of order to subtract 1 from each side.
-22 - 51x ≤ -62x
Then, we add 51x to each siding using the addition property of order
-22 ≤ -11
Lastly, we use the division property of order to divide 11 from both sides, which then gives us:
2 ≥ x
It becomes a positive because we're dividing 2 negatives, and we also turn the sign because we're dividing by negatives.
In order: Given, Distributive Property, Combine Like Terms, Subtraction Property of Order, Addition Property of Order, and Division Property of Order.
