Solving px + q = r

3x + 5 = 20 does two things to x: multiply by 3, then add 5.

Undo them backwards

The addition happened last, so undo it first. Subtract 5 from both sides.

Then undo the multiplication

3x = 15, so divide both sides by 3 to get x = 5.

Check it

3 × 5 + 5 = 20. It fits, so the answer is right.

The general two-step form

Any equation of the form px + q = r is solved by subtracting q and then dividing by p. Recognising the shape means you know both steps before you begin, which is faster and less error-prone than working it out fresh each time.

When p or q is negative

For −2x + 7 = 1, subtract 7 to get −2x = −6, then divide by −2 to get x = 3. Dividing two negatives gives a positive. The method is unchanged; only the sign arithmetic needs care.

When the answer is not whole

3x + 1 = 5 gives x = 4/3. A fractional answer is not a sign of error — most equations have them. Leaving the answer as an exact fraction is usually better than converting to a rounded decimal.

Reading the answer in context

If x is a number of buses, a solution of 4/3 means the model needs rethinking or rounding. Solving gives the mathematical answer; deciding what it means in the situation is a separate and equally necessary step.