LEARNER JOURNEY Solve x + 9 = 14
Name the goalIsolate x.
Choose the next moveSubtract 9 from both sides.
Carry out the mathematicsx = 14 − 9 = 5.
Check and interpretCheck: 5 + 9 = 14.
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
Solve equations in which one number is added to or subtracted from the variable.
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.
- inverse operation
- An operation that reverses another operation, such as subtraction reversing addition.
- constant
- A number without a variable.
Look first, then name the mathematics
Build the visual meaning
- x + a = b
- Subtract a
- Both sides
- x = b − a
- Check
Read the complete visual relationship as text
- x + a = b
- Subtract a
- Both sides
- x = b − a
- Check
Definition in plain language
For x + a = b, subtract a from both sides; equivalently, x = b − a. Treat a negative addend with its sign.
Why this matters
One-step equations make the equality-preserving logic visible before more operations are layered onto the variable.
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.
Read the signed number being added to x.
Subtract that signed number from both sides.
Simplify without dropping the sign.
Substitute the result into the original equation.
The same method in words
- Read the signed number being added to x.
- Subtract that signed number from both sides.
- Simplify without dropping the sign.
- Substitute the result into the original equation.
Interactive decision model
Build the reasoning, one decision at a time
Solve x − 7 = −2 by choosing each step.
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 x − 6 = 2
Name the goalRewrite subtraction as adding −6 if that makes the sign clearer.
Choose the next moveAdd 6 to both sides.
Carry out the mathematicsx = 2 + 6 = 8.
Check and interpretCheck: 8 − 6 = 2.
Solve x + (−4) = 11
Name the goalThe operation is adding negative 4.
Choose the next moveSubtract −4, which is the same as adding 4.
Carry out the mathematicsx = 11 − (−4) = 15.
Check and interpretCheck: 15 − 4 = 11.
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 x + (5) = 12.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
2. Solve x + (-4) = 9.
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 x + (7) = -2.
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 x + (-8) = -3.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
2. Solve x + (11) = 20.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
3. Solve x + (3) = -10.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
4. Solve x + (-6) = 15.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
5. Solve x + (14) = 5.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
6. Solve x + (-9) = -1.
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 x + (2) = 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 x + (13) = 0.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
3. Solve x + (-12) = 6.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
4. Solve x + (1) = -7.
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Write a prediction before viewing the choices.
5. Solve x + (-5) = -14.
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
Compare solving x + (−8) = 3 with solving x − 8 = 3.
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
Adding −8 and subtracting 8 mean the same thing. In either equation, add 8 to both sides to obtain x = 11. Checking gives 11 + (−8) = 3 and 11 − 8 = 3.
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.