Solving for a Variable - College

Solve for x: 4(2x + 1) + 8 = 5x

Answer:
x= - 4

Explanation:

First we must use the distributive property in order to open the parenthesis. Therefore we multiply the 4 outside the parenthesis by each term inside as follows:
8x + 4 + 8 = 5x
Now we must collect like terms, we start by adding the numbers:
8x + 12 = 5x
In order to collect the variables we must subtract 8x from both sides:
8x – 8x + 12 = 5x – 8x
12 = -3x
To solve for x, we can multiply each side of the equation by – 1/3
(- 1/3) 12 = -3 x (-1/3)
This will cancel out the –3 and we are left with:
X = - 4

In order to check our solution, we can substitute for x in the original equation. If the left side of the equation will equal the right after the substitution, then we know that we have solved it correctly. Here goes:
4[2(-4) + 1] + 8 = 5 (-4)
4[-8+1] + 8 = -20
4 [-7] + 8 = -20
-28 + 8 = -20
-20 = -20
The solution checks out ok.

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