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Grade 7 · Mathematics · 30 minutes

Unit 2 · Equations and geometric models · Lesson 1 of 2

Equations and Inequalities for a Club

Use a membership fee to separate one exact total from a spending limit.

Mr. S Teaches · Original starter mini-lesson · MS7-MATH-03

Learning objective

Solve a two-step equation and graph an inequality with a contextual whole-number solution.

Before you begin

  • Distributive property
  • Inverse operations

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

solution
A value that makes a statement true.
inequality
A comparison of unequal or possibly equal amounts.
constraint
A limit that a solution must satisfy.

Understand the concept

An equation describes one required equality; an inequality describes a range of possibilities. The same operation on both sides preserves an equation. Dividing an inequality by a positive number preserves its direction. A mathematical solution may include fractions, but a count of visits must be a nonnegative whole number.

Teach it step by step

  1. Represent a $9 joining fee plus $3 per visit as 9 + 3v. Set the total equal to $30.
  2. Subtract 9 and divide by 3; compare with the arithmetic calculation (30 − 9)/3.
  3. Change the statement to “spend less than $30” and write 9 + 3v < 30.
  4. Solve v < 7 and draw an open circle at 7 with a line to the left; identify allowable visit counts.
  5. Check the boundary v = 7 in both statements and explain why it fails the strict inequality.

Make the thinking visible

Worked example or model response

9 + 3v = 30 gives v = 7. For 9 + 3v < 30, v < 7, so allowable visit counts are 0 through 6. The point 7 is excluded because it costs exactly $30.

Guided practice

Solve 2(x + 4) = 22 by first dividing by 2. Then solve 5 + 4n > 21 and mark the solution on a number line.

Independent practice

1. Solve 4x − 6 = 18. 2. A $5 fee plus $2 per game must cost less than $17. Write and solve the inequality; give the largest allowed whole-number count.

Quick assessment

Why does a closed circle at 6 misrepresent x < 6?

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: x + 4 = 11, x = 7. For 5 + 4n > 21, n > 4; open circle at 4, shade right.
  2. Independent 1: x = 6. 2: 5 + 2g < 17, g < 6; largest count is 5 games.
  3. Quick check: A closed circle includes 6, but strict “less than” excludes it.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use a balance sketch for equations and list affordable whole-number totals before graphing.

Extension challenge

Compare a strict spending limit with “at most $17” and explain how the endpoint changes.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

7.EE.B.4.a

Common Core · Grade 7

Solve and check equations and compare algebraic and arithmetic methods.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

7.EE.B.4.b

Common Core · Grade 7

Represent a contextual inequality, graph its solution and interpret a limit.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.