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Solving Linear Equations
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Solving Linear Equations
Use inverse operations to isolate the unknown. Show your working and check solutions by substitution where asked.
Inverse operations
1.Match each operation to its inverse. For the fourth-power pair, assume the input is nonnegative.
- Add 9
- Multiply by 6
- Raise a nonnegative number to the fourth power
- Subtract 3
- Divide by 8
- Divide by 6
- Multiply by 8
- Add 3
- Subtract 9
- Take the fourth root
2.For 5x + 8 = 33, which operation should you apply to both sides first?
- Divide by 5
- Subtract 8
- Add 8
- Multiply by 5
Solve linear equations
3.Solve x + 12 = 29.
4.Solve 4a − 7 = 21. Show your working.
5.Solve 3m + 11 = 2.
6.Which sequence of steps solves 6p − 18 = 30? Select the correct sequence.
- Add 18 to both sides, then divide both sides by 6
- Subtract 18 from both sides, then divide by 6
- Divide by 6, then subtract 18
- Add 6 to both sides, then divide by 18
7.Solve 7 − 2r = 19.
Equations involving powers
8.Solve t³ − 6 = 21.
9.Solve q⁵ + 2 = 34.
10.Complete the steps for w⁴ − 10 = 6: w⁴ = after adding to each side; therefore w = after taking the root.
11.Choose all real solutions of n² − 4 = 45.
- n = 7 only
- n = −7 only
- n = ±7
- n = ±49
Check and apply
12.Test whether k = 4 satisfies 3k − 5 = 7. Substitute k = 4 and state whether both sides are equal.
TrueFalse
13.Solve 8x + 3 = 35, then check your answer by substituting it into the original equation.
14.What must be true of the two sides when a proposed solution is substituted into an equation?
15.Solve 5(y − 2) = 35. Show how you undo the multiplication and then the subtraction.
16.A cube has a volume of 125 cm³. Using V = s³, find its positive side length s.
17.Describe why applying the same operation to both sides of an equation helps preserve its equality. Include one example operation.
18.If you are stuck solving 9u − 14 = 40, name a useful first step.
4 printable pages
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