NCERT Mathematics, Class 11, textbook pages 89–99

How to help your child with Class 11 Maths Chapter 5, Linear Inequalities, at home

Solving and graphing inequalities, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

x + y ≤ 5x, y ≥ 0

NCERT Class 11 Maths Chapter 5 Linear Inequalities: what it teaches

Your teen solves linear inequalities in one variable, shows solutions on a number line, and graphs inequalities in two variables as half-planes, solving systems by shading.

Why it matters later. Inequalities lead to linear programming in Class 12.

See it: this chapter in pictures

3x − 5 < 73x < 12x < 4
Like equations, but watch the sign.
−2x ≥ 6divide by −2: flipx ≤ −3
Negative multiplier flips the sign.
test (0, 0) in x + y ≤ 50 ≤ 5 ✓shade the origin side
Test a point.

You need

  • graph paper
  • coloured pencils

Tonight’s 45 minutes

  1. Solve 3x − 5 < 7 (x < 4) and show it on a number line.
  2. Solve −2x ≥ 6: note the sign flips (x ≤ −3).
  3. Graph x + y ≤ 5 as a half-plane.
  4. Shade the region satisfying x + y ≤ 5, x ≥ 0, y ≥ 0.

Words to use

  • inequality
  • solution set
  • half-plane
  • boundary
  • shade

Watch for

  • Not flipping the sign when multiplying by a negative. Test with a number to check.
  • Solid vs dashed boundary. ≤, ≥: solid line; <, >: dashed.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You−2x ≥ 6. Divide by −2?

Your childFlip: x ≤ −3.

A game for this week: Budget region

  1. Set a budget: 2 notebooks (₹40) and pens (₹10) under ₹200.
  2. Write the inequality.
  3. Graph possible combinations.
  4. Pick the best buy.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Budget limits.
  • Speed limits.
  • Diet plans.
  • Production constraints.

Quick check

Ask these at the end of the week. Tap to see the answer.

Solve 3x − 5 < 7.

x < 4.

Solve −2x ≥ 6.

x ≤ −3.

Is (1, 1) in x + y ≤ 5?

Yes.

Ready for the next chapter when your child…

  • Solves one-variable inequalities.
  • Graphs two-variable inequalities.
  • Solves systems by shading.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 11). See the full Class 11 parent guide for every chapter.

Questions parents ask

Why does the sign flip with negatives?

Multiplying by a negative reverses order on the number line.

How do I know which side to shade?

Test a point like (0, 0).

Where are inequalities used?

Budgets, constraints and linear programming.