Mathematics • Year 7 • Unit 2 • Lesson 5

Adding and Subtracting Algebraic Terms

Build the basics: remove brackets correctly (especially when subtracting — flip every sign!), distribute a multiplier, then collect like terms to finish.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step has a short reason on the right so you can see why, not just what.

Problem. Simplify 2(3x − 1) − (x + 4) + 3.

Step 1 — Distribute the 2 into the first bracket.

2(3x − 1) = 2(3x) + 2(−1) = 6x − 2

Reason: the 2 multiplies EVERY term inside the bracket. Both 3x and the −1.

Step 2 — Remove the subtracted bracket (flip every sign).

−(x + 4) = −x − 4

Reason: a minus sign in front of a bracket flips the sign of EVERY term inside. +x becomes −x, +4 becomes −4.

Step 3 — Rewrite the whole expression without brackets.

6x − 2 − x − 4 + 3

Reason: now all the brackets are gone. The +3 at the end was never in a bracket, so it doesn't change.

Step 4 — Collect like terms.

x-terms: 6x − x = 5x Constants: −2 − 4 + 3 = −3

Reason: same as last lesson — group like terms, then add coefficients (keep variable).

Step 5 — Check with a number.

Let x = 1: original = 2(3 − 1) − (1 + 4) + 3 = 4 − 5 + 3 = 2.

My answer: 5(1) − 3 = 2 ✓

Answer: 5x − 3.

Stuck? Revisit lesson § "The Subtraction Rule" — minus in front of bracket = flip ALL signs inside.

2. We do — fill in the missing steps

Fill in each blank. 4 marks

Problem. Simplify (5x + 3) − (2x − 1).

Step 1 — Remove the first bracket (preceded by +, so signs unchanged):

(5x + 3) → ______ + ______

Step 2 — Remove the second bracket (preceded by −, so flip ALL signs inside):

−(2x − 1) → ______ + ______

Step 3 — Rewrite the full expression:

______ + ______ + ______ + ______

Step 4 — Collect like terms:

x-terms: ______ constants: ______ Final answer: ______

Stuck? The "−1" inside the second bracket becomes +1 when the bracket is removed. Two negatives make a positive.

3. You do — independent practice

Show working under each. Watch the signs when subtracting a bracket!

Foundation — single step

3.1 Simplify (x + 5) + (x + 2). 1 mark

3.2 Expand: 2(x + 4). 1 mark

3.3 Expand: 3(2a − 5). 1 mark

3.4 Remove the bracket and collect: −(3y − 7). 1 mark

Standard — combine two ideas

3.5 Simplify (4a + 2) + (3a + 5). 2 marks

3.6 Simplify (6x + 4) − (2x + 1). 2 marks

Extension — push your thinking

3.7 Simplify (5x + 3) − (2x − 1). (Watch the double subtraction!) 3 marks

3.8 Simplify 3(x + 2) + 2(x − 1). 2 marks

Stuck on 3.8? Distribute each bracket FIRST. 3(x + 2) = 3x + 6. 2(x − 1) = 2x − 2. Then add.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do ((5x + 3) − (2x − 1))

Step 1: 5x + 3.
Step 2: −(2x − 1) → −2x + 1 (flip every sign).
Step 3: 5x + 3 − 2x + 1.
Step 4: x-terms: 5x − 2x = 3x. Constants: 3 + 1 = 4. Final answer: 3x + 4.

3.1 — (x + 5) + (x + 2)

= x + 5 + x + 2 = 2x + 7.

3.2 — 2(x + 4)

= 2(x) + 2(4) = 2x + 8.

3.3 — 3(2a − 5)

= 3(2a) + 3(−5) = 6a − 15.

3.4 — −(3y − 7)

= −3y + 7 (flip both signs). Answer: −3y + 7 (or 7 − 3y).

3.5 — (4a + 2) + (3a + 5)

= 4a + 2 + 3a + 5 = 7a + 7.

3.6 — (6x + 4) − (2x + 1)

Drop first bracket: 6x + 4. Flip second: −2x − 1. Together: 6x + 4 − 2x − 1 = 4x + 3.

3.7 — (5x + 3) − (2x − 1)

Drop first: 5x + 3. Flip second: −2x + 1 (the −1 becomes +1). Together: 5x + 3 − 2x + 1 = 3x + 4. (Watch — the double negative becomes positive.)

3.8 — 3(x + 2) + 2(x − 1)

Distribute: 3(x + 2) = 3x + 6. 2(x − 1) = 2x − 2. Add: 3x + 6 + 2x − 2 = 5x + 4.