Solving step by step

Solving step by step

Solving linear equations step by step

The same recipe works for every linear equation in grade 7:

**Undo operations one by one, in reverse order, while doing the same

thing to both sides.**

px + q = r — two steps

3x + 5 = 14
  1. Subtract 5 from both sides → `3x = 9`.
  2. Divide by 3 on both sides → `x = 3`.

That order matters: you "peel off" the outermost operation first.

Here the outermost was the `+ 5`, so we undo that before the `·3`.

p(x + q) = r — two paths

3(x + 2) = 18
Path A — expand first: 
3x + 6 = 18    (distribute)
3x = 12        (subtract 6)
x = 4          (divide by 3)
Path B — divide first: 
x + 2 = 6      (divide by 3)
x = 4          (subtract 2)

Both arrive at `x = 4`. Use Path B when `r` is divisible by p —

it's faster.

ax + b = cx + d — collect like terms

2x + 5 = x + 11
  1. Subtract `x` from both sides → `x + 5 = 11`.
  2. Subtract 5 from both sides → `x = 6`.

Tip: subtract the smaller x-coefficient. That always leaves a

positive coefficient in front of `x` and avoids sign mistakes.

One-step inequalities

x + 3 > 7

Subtract 3 from both sides → `x > 4`.

Important — adding/subtracting the same number does not flip the

inequality. Multiplying or dividing by a negative number does

(we leave that for grade 8).

Checking your answer

After solving, substitute back into the original equation:

3 · 3 + 5 = 9 + 5 = 14  ✓

A quick check catches typos and sign mistakes — always worth 5 seconds.

Try it yourself