LEARNER JOURNEY Solve 5x + 2 = 2x + 14
Name the goalCollect variable terms on one side.
Choose the next moveSubtract 2x from both sides.
Carry out the mathematics3x + 2 = 14, then 3x = 12 and x = 4.
Check and interpretCheck: 22 = 22.
Start here
Build the concept from the beginning
Starting point
No prior equation-solving skill is assumed. Arithmetic operations, variables, equality, and every new algebra decision are explained on this page.
Learning target
Collect variable terms on one side and constants on the other before isolating x.
Evidence of mastery
Construct the reasoning path, solve at least 4 of 5 mastery problems, and revise an unfamiliar explanation.
Essential terms
- equation
- A statement that two mathematical expressions have the same value.
- solution
- A value that makes an equation true when substituted for the variable.
- coefficient
- A numerical factor multiplying a variable.
- constant
- A number without a variable.
Look first, then name the mathematics
Build the visual meaning
- Variable terms
- Subtract from both sides
- Collect constants
- Isolate x
- Check
Read the complete visual relationship as text
- x on both sides
- Subtract same x-term
- Collect variables
- Collect constants
- Solve
Definition in plain language
When x appears on both sides, add or subtract a variable term from both sides to create one side with variable terms and one side with constants.
Why this matters
The variable has not changed sides magically; matched operations create an equivalent equation with fewer variable terms.
Reasoning path
See the method as a sequence
Move from left to right. Each decision prepares the next one; on a phone, follow the numbered cards from top to bottom.
Simplify both sides separately.
Subtract one variable term from both sides.
Move constants using matched operations.
Divide by the remaining coefficient and check.
The same method in words
- Simplify both sides separately.
- Subtract one variable term from both sides.
- Move constants using matched operations.
- Divide by the remaining coefficient and check.
Interactive decision model
Build the reasoning, one decision at a time
Solve 6x + 1 = 2x + 17.
Choose this step, then check the construction.
Choose this step, then check the construction.
Choose this step, then check the construction.
The reasoning path changes as each decision is selected.
Choose every step, then check the construction.
Model before practice
Three fully explained examples
Every example identifies the goal, explains the next move, carries out the algebra, and checks or interprets the result.
Solve 7x − 5 = 4x + 10
Name the goalKeep the larger positive x-coefficient if convenient.
Choose the next moveSubtract 4x, then add 5.
Carry out the mathematics3x = 15, so x = 5.
Check and interpretCheck: 30 = 30.
Solve −2x + 9 = 3x − 6
Name the goalEither side can hold the variable; choose steps that reduce sign errors.
Choose the next moveAdd 2x to both sides and add 6.
Carry out the mathematics15 = 5x, so x = 3.
Check and interpretCheck: 3 = 3.
Practice with decreasing support
Guided practice
Practice immediately after the model
Predict first. Then use the visual relationship and reasoned feedback to check two decisions.
1. Solve 5x + (3) = 2x + (15).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
2. Solve 7x + (-2) = 3x + (-6).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
Not completed yet.
Partially completed problem
Finish the missing step
A prompt supplies part of the reasoning. Predict the missing mathematical move before choices appear.
1. Solve -2x + (5) = 4x + (-13).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
Not completed yet.
Independent practice
Six problems for repetition
Solve all six. Use the specific feedback to revise a method or sign error.
1. Solve 6x + (1) = -3x + (-17).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
2. Solve 4x + (-7) = 1x + (8).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
3. Solve -5x + (2) = -1x + (14).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
4. Solve 8x + (4) = 2x + (40).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
5. Solve 3x + (-5) = -2x + (30).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
6. Solve -4x + (9) = 2x + (15).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
Not completed yet.
Mastery and transfer
Mastery check
Demonstrate understanding
Attempt all five. At least four correct answers are required for mastery.
1. Solve 9x + (-3) = 5x + (5).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
2. Solve 2x + (6) = -3x + (-14).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
3. Solve -7x + (-1) = -2x + (-26).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
4. Solve 10x + (8) = 4x + (-4).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
5. Solve 5x + (-6) = -1x + (12).
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
Not completed yet.
Unfamiliar transfer
Explain, compare, and revise
Solve 3x + 11 = 7x − 5 using two different valid first steps.
Guided self-check
Judge the locked first attempt against every criterion. Each judgment gives revision guidance.
Choose Met or Needs revision.
Choose Met or Needs revision.
Choose Met or Needs revision.
Model reasoning
Subtracting 3x first gives 11 = 4x − 5, then 16 = 4x and x = 4. Subtracting 7x first gives −4x + 11 = −5, then −4x = −16 and x = 4. Both paths preserve equality and check in the original equation.
Write a first attempt before opening the self-check.
The record reveals exact answers and model reasoning only after the corresponding attempt or self-check has occurred.