Learn with Amar
Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Translate absolute value into distance from a center.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
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 |x−3|=5.
Why this math matters
Translate a fixed-distance condition into possible positions on a number line. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
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.
Solve a distance equation with two directions
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Solve |x−3|=5.
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 conditions
Distance from x to 3 is 5
Absolute value measures a nonnegative gap.
Develop the calculation
x−3=5 or x−3=−5
The point can lie five units on either side.
Check and interpret
x=8 or x=−2
Both substitutions give an absolute difference of five.
The result
x=8 or x=−2
Both substitutions give an absolute difference of five.
Common mistakes to catch
- Keep both distance directions unless the distance is zero.
- An absolute value cannot equal a negative number.
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 |y+1|=4.
Show a hint
The center is negative one.
Reveal answer and explanation
y=3 or y=−5
Both points lie four units from −1.
Practice 2
How many real solutions does |x−2|=−3 have?
Show a hint
Distance cannot be negative.
Reveal answer and explanation
None
The left side is always nonnegative and cannot equal −3.
Take the idea with you
Translate a fixed-distance condition into possible positions on a number line.
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.
Up next: One input must have one output
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