Example
Solve:
3x−7−2x−4=1
Solution:
The left side of the equation has an expression that we should simplify before trying to isolate the variable.
| 3x−7−2x−4=1 |
Rearrange the terms, using the Commutative Property of Addition. | 3x−2x−7−4=1 |
Combine like terms. | x−11=1 |
Add 11 to both sides to isolate x . | x−11+11=1+11 |
Simplify. | x=12 |
Check.Substitute x=12 into the original equation.
3x−7−2x−4=1
3(12)−7−2(12)−4=1
36−7−24−4=1
29−24−4=1
5−4=1
1=1✓
The solution checks.
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Now you can try solving a couple equations where you should simplify first.
example
Solve:
3(n−4)−2n=−3
Answer:
Solution:
The left side of the equation has an expression that we should simplify.
| 3(n−4)−2n=−3 |
Distribute on the left. | 3n−12−2n=−3 |
Use the Commutative Property to rearrange terms. | 3n−2n−12=−3 |
Combine like terms. | n−12=−3 |
Isolate n using the Addition Property of Equality. | n−12+12=−3+12 |
Simplify. | n=9 |
Check.Substitute n=9 into the original equation.
3(n−4)−2n=−3
3(9−4)−2⋅9=−3
3(5)−18=−3
15−18=−3
−3=−3✓
The solution checks.
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Now you can try a few problems that involve distribution.
example
Solve:
2(3k−1)−5k=−2−7
Answer:
Solution:
Both sides of the equation have expressions that we should simplify before we isolate the variable.
| 2(3k−1)−5k=−2−7 |
Distribute on the left, subtract on the right. | 6k−2−5k=−9 |
Use the Commutative Property of Addition. | 6k−5k−2=−9 |
Combine like terms. | k−2=−9 |
Undo subtraction by using the Addition Property of Equality. | k−2+2=−9+2 |
Simplify. | k=−7 |
Check.Let k=−7.
2(3k−1)−5k=−2−7
2(3(−7−1)−5(−7)=−2−7
2(−21−1)−5(−7)=−9
2(−22)+35=−9
−44+35=−9
−9=−9✓
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The solution checks.
Now, you give it a try!