Solving linear equations GCSE lesson: balance, brackets, both sides, fractions

Linear equations: practice

Write one equation a line, and say to yourself what you did to both sides. Each line is checked as you write it. End with x = … (write x = 3, not 3 = x). The stretch is optional.

Diagnostic question: choose and explain

1. Solve 5x − 3 = 2x + 9.
   1. x = 2
   2. x = 4
   3. x = 12/7
   4. x = 9

Practice questions

1. Solve 3x + 7 = 22, one step a line.They solve 3x + 7 = 22 line by line, each line checked as they write it.
2. Solve x/4 − 3 = 2, one step a line.They solve x/4 − 3 = 2 line by line, each line checked as they write it.
3. Solve 5(x − 2) = 3x + 4, one step a line.They solve 5(x − 2) = 3x + 4 line by line, each line checked as they write it.
4. Solve 7 − 2x = 3x − 8, one step a line.They solve 7 − 2x = 3x − 8 line by line, each line checked as they write it.
5. Each line was written as a first step for 3x + 4 = 2x + 9. Which keep the balance, and which break it?They sort 6 items into Keeps the balance and Breaks it.
6. Solve 4x + 3 = 5. Then drag the marker to the solution on the number line.They drag a marker on a number line from -2 to 3.
7. Solve (x + 5)/3 = x − 1, one step a line.They solve (x + 5)/3 = x − 1 line by line, each line checked as they write it.
8. A rectangle is x cm wide and (x + 4) cm long. Its perimeter is 30 cm. Form an equation and solve it to find x. Give your answer as a decimal.
9. I think of a number. Three times it, take away 4, is the same as the number add 10. My number is ___.
10. Stretch: solve (2x − 1)/3 − (x + 2)/4 = 1, one step a line. Your answer may be a fraction.They solve (2x − 1)/3 − (x + 2)/4 = 1 line by line, each line checked as they write it.

Support: For question 3: expand the bracket first, multiplying both terms inside by 5. Then take 3x from both sides, then add 10 to both sides, then divide.

Linear equations: exit

One equation a line, ending with x = …. One sentence for the second question.

1. Solve 4(x − 1) = 2x + 6, one step a line.They solve 4(x − 1) = 2x + 6 line by line, each line checked as they write it.
2. In words: what did you do to both sides in your first line, and why does that keep the answer the same?

Exit check

One equation solved line by line, and one sentence, show who keeps the balance.

Solve 4(x − 1) = 2x + 6, one step a line.

Linear equations: keep the balance

Write one step a line, and beside each line what you did to both sides. Check every answer by putting it back into the first line. For question 6, form the equation first.