Example 1
Graph x ≥ −2.
- Closed circle at −2 (it is included).
- Shade to the right (greater).
- Every number from −2 upwards.
Answer: ● at −2, shaded right
⚖️ Grade 7 · equations · session 7 of 12 · 60 minutes · ⭐ Plus
Solving and graphing inequalities px + q > r
An inequality has many solutions: x > 4 means every number bigger than 4. Solve it like an equation, but when you multiply or divide by a negative number, flip the sign. Then graph it.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up4 min
- Reading and graphing9 min
- Solving like an equation9 min
- Negatives and word problems9 min
- Activity 17 min
- Activity 27 min
- Activity 35 min
- Quiz6 min
- Set the project4 min
By the end you can
- Read and graph x > a, x ≥ a, x < a and x ≤ a
- Solve px + q > r, flipping the sign when dividing by a negative
- Write and interpret inequalities from word problems
- NJSLS-M 7.EE.B.4.b (Common Core 7.EE.4)
Before you start
- Solving equations px + q = r
- Number lines with negatives
Have ready
- The inequality number line on screen
Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE
Warm-up · think first
You must be at least 120 cm tall for a ride. Write that as an inequality for your height h.
Show the answer
h ≥ 120: 120 cm is allowed, so the sign includes 'equal to'.
Teacher tip: Ask for other 'at least' and 'less than' rules from real life.
Part 1 of 3 · learn, see, practise
Reading and graphing inequalities
> greater than, < less than, ≥ greater than or equal to, ≤ less than or equal to.
On a number line: open circle ○ when the number is not included (>, <); closed circle ● when it is (≥, ≤).
Shade the direction of the solutions: right for greater, left for less.
Inequality number line
Tap a number to move the circle, then choose open or closed and the direction.
- Graph x > 4.
- Graph x ≤ −3.
- Graph x ≥ 0.
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Answers (for the teacher)
- no
- yes
- open
- x ≤ 7
- -2
⭐ Part of Pure Faith Plus
The rest of this lesson is in Plus
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You have seen the plan, the warm-up and part 1. With Plus you also get:
- Part 2: Solving like an equation, with practice at three levels
- Part 3: Negatives flip the sign, and word problems, with practice at three levels
- Class activity 1: Solve and graph
- Class activity 2: True or false?
- Class activity 3: Budget limits
- A 8-question quiz
- After-class project: Rules of the park
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Solving and graphing inequalities px + q > r: questions
How do you solve px + q > r?
Undo q on both sides, then divide by p. If p is negative, reverse the inequality sign.
Why does the sign flip with a negative?
Multiplying by a negative reverses order: 2 < 3 but −2 > −3.
Which standard is this?
New Jersey 7.EE.B.4.b (Common Core 7.EE.4b).
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