Worked example
Example 1: Undo operations in reverse order
Problem
What value of solves ?
Subtract 4: .
Which inverse operation or rearrangement is valid?
Which substitution makes the original equation true?
Unit 3 · Linear RelationshipsA2 · Linear Equations · Structures
Linear Equations & Literal Formulas
Solve linear equations cleanly and rearrange formulas for any variable.
Ready when you are
7 steps · about 29 minutes
Start with the warm-up.
StartStep 1 of 7Warm-upDone
Warm-up
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Key terms
- Coefficient
- A number multiplying a variable.
- Literal equation
- A formula with several letters solved for one target letter.
- Solution
- A value that makes the original equation true.
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Step 2 of 7Try it firstDone
Try it first
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Take a shot before the lesson. Write one relationship from the stem, even if you do not finish.
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Step 3 of 7LearnDone
The big idea
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See the structure
An equation is a balance. Simplify each side, move variable terms together, then undo addition and multiplication in reverse order.
Key idea
Name quantities before calculating
Write what each number measures. A correct calculation with the wrong quantity or unit still misses the question.
Build a reliable method
A literal formula uses the same moves with letters. Treat the target letter as the variable and everything else as a constant.
Explore in Desmos
Read and verify a linear solution
Click the intersection to read , so solves . Substitute 3 into the original left side; algebra is faster here, while the graph is a useful check.
The calculator is live: change anything and see what happens.
Read and verify a linear solution
Degree modePress Escape to leave the calculator (twice if a menu is open).
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Stretch to a 36
Graphing the whole equation in Desmos produces a vertical solution line. Algebra is faster for one-step equations; Desmos is excellent for messy coefficients and checking.
Trap
A believable answer to the wrong question
The choices often include a correct intermediate number. Before selecting it, reread the highlighted ask and check the unit, sign, and domain.
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Step 4 of 7Worked examplesDone
Worked examples
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Skip check · 2 questions
Already know this? Get both right on the first try and you can skip the worked examples.
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Skipped ahead. The worked examples stay here if you want them later.
Divide by : .
Worked example
Example 2: Rearrange a literal formula
Problem
Which expression equals when ?
Multiply by 2: .
Which inverse operation or rearrangement is valid?
Which substitution makes the original equation true?
Faded example · you finish it
Example 3: Complete the setup and result
Problem
What value of solves ?
Choose the setup that follows the stated relationship.
Choose the resulting value.
Desmos way
Solve an equation at an intersection
Graph
y=5(x-2)+3 and y=28. Click the intersection and read its -coordinate, 7.Substitute to verify: . The graph checks the result, while inverse operations explain why it is the only solution.
Solve an equation at an intersection
Degree modePress Escape to leave the calculator (twice if a menu is open).
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Step 5 of 7PracticeDone
Practice
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Step 6 of 7Spot the mistakeDone
Spot the mistake
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Spot the mistake
Where did it go wrong?
One line has an error. Click the line where it first goes wrong.
What went wrongSubtracting 4 from 19 gives 15, so .
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Step 7 of 7Exit ticketDone
Exit ticket
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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36
These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.