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Solve:
Here the variable, is on both sides, but the constants appear only on the right side, so let’s make the right side the “constant” side. Then the left side will be the “variable” side.
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| We don't want any variables on the right, so subtract the . |
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| Simplify. |
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| We have all the variables on one side and the constants on the other. We have solved the equation. | ||
| Check: |
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| Substitute 7 for . |
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Solve:
The only constant, is on the left side of the equation and variable, is on both sides. Let’s leave the constant on the left and collect the variables to the right.
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| Subtract from both sides. |
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| Simplify. |
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| We have the variables on the right and the constants on the left. Divide both sides by 2. |
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| Simplify. |
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| Rewrite with the variable on the left. |
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| Check: Let . | |
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Solve:
The only constant, is on the right, so let the left side be the variable side.
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| Remove the from the right side by adding to both sides. |
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| Simplify. |
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| All the variables are on the left and the constants are on the right. Divide both sides by 8. |
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| Simplify. |
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| Check: Substitute . | |
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The next example will be the first to have variables and constants on both sides of the equation. As we did before, we’ll collect the variable terms to one side and the constants to the other side.
Solve:
Start by choosing which side will be the variable side and which side will be the constant side. The variable terms are and Since is greater than make the left side the variable side and so the right side will be the constant side.
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| Collect the variable terms to the left side by subtracting from both sides. |
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| Simplify. |
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| Now, collect the constants to the right side by subtracting 5 from both sides. |
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| Simplify. |
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| The solution is . | |
| Check: Let . | |
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We’ll summarize the steps we took so you can easily refer to them.
It is a good idea to make the variable side the one in which the variable has the larger coefficient. This usually makes the arithmetic easier.
Solve:
We have on the left and on the right. Since make the left side the “variable” side.
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| We don't want variables on the right side—add to both sides to leave only constants on the right. |
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| Combine like terms. |
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| We don't want any constants on the left side, so add 2 to both sides. |
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| Simplify. |
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| The variable term is on the left and the constant term is on the right.
To get the coefficient of to be one, divide both sides by 9. |
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| Simplify. |
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| Check: Substitute 1 for . | |
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