11) Justify each of the following manipulations to combine two expressions by filling in the blanks with the associative property, the commutative property, or the distributive property.

5(2x + 1) +2(3x + 4) = (10x + 5) + 2(3x+4)
= (10x + 5)+(6x+8)
= 10x + (5 +6x)+8
= 10x +(6x + 5)+8
= (10x +6x)+(5+8)
= (10+6)x+(5+8)
= 16x +13

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Step-by-step explanation:

Simplifying

10x + -4 = 6x + 8

Reorder the terms:

-4 + 10x = 6x + 8

Reorder the terms:

-4 + 10x = 8 + 6x

Solving

-4 + 10x = 8 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

-4 + 10x + -6x = 8 + 6x + -6x

Combine like terms: 10x + -6x = 4x

-4 + 4x = 8 + 6x + -6x

Combine like terms: 6x + -6x = 0

-4 + 4x = 8 + 0

-4 + 4x = 8

Add '4' to each side of the equation.

-4 + 4 + 4x = 8 + 4

Combine like terms: -4 + 4 = 0

0 + 4x = 8 + 4

4x = 8 + 4

Combine like terms: 8 + 4 = 12

4x = 12

Divide each side by '4'.

x = 3

Simplifying

x = 3

594 square inches

step-by-step explanation:

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