Learn with Amar
Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to reverse an inequality when dividing by a negative.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
One-step equations and comparison symbols.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Solve −3x + 2 < 14 and use one included and one excluded value to check the result.
Why this math matters
Multiplying or dividing an inequality by a negative reflects the number line and reverses order. Check a boundary value and a value on each side when graphing an inequality solution.
Set up the model
A useful answer starts with clear assumptions:
- x is real.
- The inequality is strict, so equality is excluded.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Reverse an inequality when dividing by a negative
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Solve −3x + 2 < 14 and use one included and one excluded value to check the result.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
−3x < 12
Subtract 2 from both sides without changing their order.
Apply the relationship
x > −4
Dividing by −3 reverses the inequality sign.
Check and interpret
x = 0 gives 2 < 14; x = −5 gives 17 < 14, which is false
The solution consists of values to the right of −4, without −4 itself.
The result
x = 0 gives 2 < 14; x = −5 gives 17 < 14, which is false
The solution consists of values to the right of −4, without −4 itself.
Common mistakes to catch
- Adding or subtracting a negative does not trigger the reversal rule.
- A strict inequality requires an open boundary, not an included endpoint.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Solve −2y ≥ 10.
Show a hint
Divide by −2 and reverse the comparison.
Reveal answer and explanation
y ≤ −5
The equality remains allowed, while the direction reverses.
Practice 2
Does x = −4 satisfy the original inequality?
Show a hint
Substitute into −3x + 2 < 14.
Reveal answer and explanation
No
The left side equals 14, and 14 < 14 is false.
Take the idea with you
Check a boundary value and a value on each side when graphing an inequality solution.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
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