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Year 7AC9M7A03

Solving Equations and Checking

Solve one-variable linear equations with natural number solutions; verify the solution by substitution.

Solving means getting the letter alone. Whatever you do to one side you must do to the other, and then you check by putting your answer back in.

Method

Do the same to both sides
That is the only rule. Everything else follows from it.
Undo with the opposite operation
+×÷+ \leftrightarrow - \qquad \times \leftrightarrow \div
Work backwards through what was done to the letter.
Always verify by substitution
It costs ten seconds and catches every arithmetic slip.

Worked example

e.g. Solve 4x+5=21\text{Solve } 4x + 5 = 21
  1. Look at what has been done to xx: multiplied by 4, then 5 added.×4 then +5\times 4 \ \text{then} \ +5
  2. Undo the last step first. Subtract 5 from both sides.4x+55=2154x + 5 - 5 = 21 - 5
  3. Simplify.4x=164x = 16
  4. Undo the multiplication. Divide both sides by 4.x=4x = 4
  5. Verify by substituting back into the original equation.4(4)+5=214(4) + 5 = 21 \quad\checkmark

Practice

Solve, then verify by substitution.

1
x+7=12x + 7 = 12
Answerx=5x = 5
2
3y=273y = 27
Answery=9y = 9
3
m4=6\frac{m}{4} = 6
Answerm=24m = 24
4
2a3=112a - 3 = 11
Answera=7a = 7
5
A learner says x=5 solves 3x+2=20. Check it.\text{A learner says } x=5 \text{ solves } 3x+2=20. \text{ Check it.}
Answer3(5)+2=1720wrong; x=63(5)+2 = 17 \neq 20 \quad\therefore\quad \text{wrong; } x=6
Next step
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