Grade 7 · lesson 2 of 4

Combine Like Terms without Losing Signs

Like terms have the same variable part and exponent.

About 20 minutes, plus any extended practice

Supplied materials

Paper or a browser scratch area; a calculator is optional unless rounding is requested.
Supplied teaching case: Simplify 2x+3−5x+2. Candidate answers: (A) -3x+1 (B) -3x+5 (C) 2x (D) 7x+5.
Independent check inputs: Simplify 3x+4−7x+3. Candidate answers: (A) -4x+1 (B) -4x+7 (C) 10x+7 (D) 3x.

Learn the idea

An expression names a quantity without asserting equality to another quantity. Equivalent expressions give the same output for every allowed input, and their structures can reveal repeated groups, fixed extras, or shared factors. Like terms have the same variable part and exponent. Their coefficients can be combined, while constants form a separate group; subtraction contributes a negative coefficient.

Here is the method on the supplied teaching case. Combine like x terms: (2−5)x=-3x. Combine constants separately: 3+2=5. The result is -3x+5.

An x-term and a constant do not combine into one x-term. Keep coefficients and constants in separate columns if needed; the minus sign before a term belongs in its coefficient.

Write or sketch the supplied teaching case, labeling its quantities and restrictions.
Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
Solve the independent check with its changed inputs before revealing feedback.
Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Worked example

See the method in action

Teaching case: Simplify 2x+3−5x+2. Candidate answers: (A) -3x+1 (B) -3x+5 (C) 2x (D) 7x+5. Solution: Combine like x terms: (2−5)x=-3x. Combine constants separately: 3+2=5. The result is -3x+5. The final answer is -3x+5. An x-term and a constant do not combine into one x-term. Keep coefficients and constants in separate columns if needed; the minus sign before a term belongs in its coefficient.

Your turn

Check your reasoning

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Helpful tips

Like terms have the same variable part and exponent.
An x-term and a constant do not combine into one x-term.

See the answer and explanation

-4x+7

Combine like x terms: (3−7)x=-4x. Combine constants separately: 4+3=7. The result is -4x+7.

Take it further

Changed-input task: Simplify 9x+10−19x+9. Candidate answers: (A) -10x+1 (B) -10x+19 (C) 28x+19 (D) 9x. Show the mathematical reason, not only the selected answer. Expected result: -10x+19. Combine like x terms: (9−19)x=-10x. Combine constants separately: 10+9=19. The result is -10x+19.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

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