01Why this matters
Equations help work backwards from a known total to an unknown amount, such as a number of tickets or a length.
02See it
03Understand it
A linear equation has variables only to the first power. Solving it means finding values that make both sides equal.
Think of equality as a balanced scale. Performing the same reversible operation on both sides keeps it balanced. Undo addition or subtraction first when it sits outside a multiplication, then undo the multiplication or division. Check your solution in the original equation.
04Guided example
Solve 3x + 5 = 20.
- Subtract 5 from both sides to remove the added constant: 3x = 15.
- Divide both sides by 3 to undo multiplication: x = 5.
- Check: 3 × 5 + 5 = 20. The left side matches the right side.
05Try it
06Practise it
07Use it in the real world
A $5 entry fee plus $3 per ride totals $20. The equation 5 + 3r = 20 shows that the visitor paid for 5 rides.
Go a little deeper
Some equations have no solution, such as x + 1 = x + 2. Others are true for every allowed x, such as 2(x + 1) = 2x + 2.
08Quick check
09Summary
A linear equation has variables only to the first power. Solving it means finding values that make both sides equal. Check: 3 × 5 + 5 = 20. The left side matches the right side.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
ax + b = c → x = (c − b)/a
a is a non-zero coefficient; b and c are constants; x is the unknown.
c = ax + b
Find this in the formula library →