9514 1404 393
Answer:
- x = 7
- x = 4
- x = 5
- x = 2
Explanation:
The general steps are ...
- look at what you have
- rewrite the equation so the variable terms are on one side and the constant terms are on the other side of the equal sign; collect terms
- divide by the coefficient of the variable
It is generally convenient to put the variable terms on the side of the equation having the largest (most positive) variable term. You do the rearranging by subtracting the terms you don't want. Any operation is performed on both sides of the equation.
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1) 3x + 7 = 4x
We observe the largest x-term is on the right, and the only constant term is on the left. We can subtract the x-term 3x to eliminate it from the left side
3x +7 -3x = 4x -3x
Combining like terms gives ...
7 = x . . . . . this is the solution
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2) x +2 +2x = x + 10
We observe x-terms and constants on both sides of the equation. First of all, we will combine like terms.
3x +2 = x +10
The largest x-term is on the left, so we choose to subtract x (the x-term on the right)
3x -x +2 = x -x +10
2x +2 = 10
We don't want the constant on the left, so we subtract 2.
2x +2 -2 = 10 -2
2x = 8 . . . . . . . . . . combine like terms
Now, we divide by the coefficient of x.
2x/2 = 8/2
x = 4 . . . . . . the solution
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3) x +3x = x + x + 10
4x = 2x +10 . . . . . . . combine like terms
2x = 10 . . . . . . . . . . . subtract 2x
x = 5 . . . . . . . . . . . . . divide by 2
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4) 2x +3 + 3x = x + 11
5x +3 = x +11 . . . . . . . . combine like terms
4x +3 = 11 . . . . . . . . . . . subtract x
4x = 8 . . . . . . . . . . . . . . subtract 3
x = 2 . . . . . . . . . . . . . . .divide by 4
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Learn to identify and combine like terms. Use addition or subtraction to eliminate terms you don't want. Use multiplication or division to eliminate coefficients you don't want. Whatever you do to one side of the equation must also be done to the other side of the equation. (In the above, we use "subtract ..." to mean "subtract ... from both sides of the equation," for example.)