Simplify using the distributive property, Show all work -2(x - 5) + 4(9 + x).

Solution:

Given,

Equation is -2(x - 5) + 4(9 + x).

Definition:

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parentheses.

The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.

This property can be stated symbolically as:

A (B + C) = AB + AC.

Use the distributive property to multiply -2 by x - 5.

= -2x + 10 + 4(9 + x).

Use the distributive property to multiply 4 by 9 + x.

= -2x + 10 + 36 + 4x.

Add 10 and 36 to get 46.

= -2x + 46 + 4x.

Combine -2x and 4x to get 2x.

= 2x + 46.

Therefore, the solution is 2x + 46.

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Simplify using the distributive property, Show all work -2(x - 5) + 4(9 + x).

Summary:

Simplifying using the distributive property, and showing all the work for -2(x - 5) + 4(9 + x), we get the solution as 2x + 46.