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Grade 6 · lesson 2 of 4

Substitute a Value While Preserving Expression Structure

Write the supplied value in place of each variable, using parentheses to prevent ambiguous notation.

About 20 minutes, plus any extended practice

Download the grade pack

Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: For 3x²+4 at x=2, write 3×(2²)+4=3×4+4=16.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A variable is a symbol representing a number. Evaluation replaces every occurrence with the supplied value, preserving grouping and operation order. A coefficient next to a variable means multiplication. An expression has a value after substitution, but it is not an equation claiming equality to a second expression.

Write the supplied value in place of each variable, using parentheses to prevent ambiguous notation. Evaluate powers and grouped parts before later operations. Check all variable occurrences were replaced and keep the original input value recorded.

Replace every variable occurrence with the same supplied input. A coefficient outside x² is not automatically part of the squared base. Write a full substitution line before simplifying any arithmetic.

  1. Write a full substitution line before simplifying any arithmetic.
  2. Work through the supplied example and label what each number or attribute represents.
  3. Write the supplied value in place of each variable, using parentheses to prevent ambiguous notation.
  4. Answer the check, then try the three changed-input practice questions and explain one correction.
Worked example

See the method in action

For 3x²+4 at x=2, write 3×(2²)+4=3×4+4=16. Writing (3×2)²+4 would square the coefficient as well and change the expression. The input is two; sixteen is the resulting value. Replace every variable occurrence with the same supplied input. A coefficient outside x² is not automatically part of the squared base. Write a full substitution line before simplifying any arithmetic.

Your turn

Check your reasoning

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Helpful tips
  • Replace every variable occurrence with the same supplied input.
  • A coefficient outside x² is not automatically part of the squared base.
Evaluate 2x²+3 for x=2.

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

11

Replace x, square its value, then multiply by two and add three. The result is 11.

Take it further

Evaluate 4(y+2) for y=3. Expected: 20.

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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.

More practice: try new cases
1. Evaluate 2x²+3 for x=3.
Need a hint?
  • Replace every variable occurrence with the same supplied input.
  • A coefficient outside x² is not automatically part of the squared base.
2. Evaluate 2x²+3 for x=4.
Need a hint?
  • Replace every variable occurrence with the same supplied input.
  • A coefficient outside x² is not automatically part of the squared base.
3. Evaluate 2x²+3 for x=5.
Need a hint?
  • Replace every variable occurrence with the same supplied input.
  • A coefficient outside x² is not automatically part of the squared base.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.