Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Collect variable terms through equality-preserving operations.
- 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 5x − 7 = 2x + 14.
Why this math matters
Compare two linear models by solving the input at which their outputs agree. 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 when the variable appears on both sides
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Solve 5x − 7 = 2x + 14.
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
Subtract 2x: 3x − 7 = 14
Apply the same subtraction to both expressions.
Develop the calculation
Add 7: 3x = 21
Remove the remaining constant from the variable side.
Check and interpret
x = 7; both original sides equal 28
Division by three isolates x and substitution verifies it.
The result
x = 7; both original sides equal 28
Division by three isolates x and substitution verifies it.
Common mistakes to catch
- Do not move a term without accounting for the operation that changes its sign.
- Check in the original equation rather than only the last simplified line.
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 4y + 9 = y − 6.
Show a hint
Subtract y and then nine.
Reveal answer and explanation
y = −5
3y=−15, so y=−5; both sides become −11.
Practice 2
A learner adds 7 only to the left of the main equation. What principle is violated?
Show a hint
Equality must be preserved.
Reveal answer and explanation
Both sides need the same operation
Changing only one side generally changes which inputs satisfy the equation.
Take the idea with you
Compare two linear models by solving the input at which their outputs agree.
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: An equation can have all, one, or no solutions
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