Answer:
- simplifies to 4x +8 = 16
- has solution x = 2
Explanation:
The equation is simplified by combining "like" terms. The terms "2x" and "2x" are "like" not just because they are identical, but because the only variable (x) is raised to the same power (1) in each term. We can use the distributive property to help combine those terms:
2x +2x = (x)(2+2) = 4x
Of course, the constants on the left can be simply added: 3 + 5 = 8.
Now, the simplified form of the equation is ...
4x + 8 = 16
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To solve this, we note that all the numerical values are multiples of 4, the x-coefficient. Then we can divide all of them by 4 to give ...
x + 2 = 4
You know the value of x already at this point, since you're familiar with your addition facts. However, to complete the solution algebraically, we subtract 2 from both sides of the equation:
x = 2
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Comment on this solution
You will usually get instruction to "separate the variable terms from the constant terms," so the simplified equation would usually have 8 subtracted from both sides to give ...
4x = 8
Then, you would divide by the x-coefficient to get x=2.
I elected to do it the way shown above for a couple of reasons:
- so you can see it is possible and gives the correct result
- so the numbers remaining in the equation are smaller, making the math slightly easier