Solve one-step equations

Objective. Solve equations using inverse operations.

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2. Worked example
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Learn: the key idea

A one-step equation can be solved using a single inverse operation to isolate the variable. If the equation involves addition, subtract the same amount from both sides; if it involves multiplication, divide both sides by the same number. For example, to solve x+7=15, subtract 7 from both sides to get x=8. Similarly, to solve 5x=30, divide both sides by 5 to get x=6. Whatever operation is performed must be done to both sides of the equation to keep it balanced.

Worked example

Solve the one-step equation 9x = 54.

1 $Identify the operation linking x to 54: multiplication by 9.$
2 $Apply the inverse operation to both sides: divide by 9.$
3 $Calculate: 54\div9=6.$
4 $Check by substituting back: 9\times6=54.$

Answer: x = 6

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Common mistake. Pupils sometimes apply the inverse operation to only one side of the equation, turning x+7=15 into x=15+7 instead of x=15−7. Always apply the same operation to both sides together.

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