Question 1 of 3Both examsAI-A.REI.3Algebra I Regents · June 2024 · Q6Non-calculatorproficient
The solution to 4(x − 5)/3 + 2 = 14 is
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Unit 4 · Solving Linear Equations & Inequalities
Solving Linear Equations
Use inverse operations, keeping the equation balanced. If variables cancel, interpret the remaining true or false statement.
NY-8.EE.7AI-A.REI.3AI-A.CED.1
Notes
Balance, don't hop
Whatever you do to one side, do to the other. Distribute first, combine like terms, collect variable terms, then isolate.
Special cases
If you obtain 0 = 0, every real number works (identity). If you obtain 0 = 5, there is no solution. Algebra I also solves ax + b = c with letter coefficients.
Vocabulary
identity
An equation true for all values of the variable.
Example: 2(x + 3) = 2x + 6 is an identity.
no solution
An equation that is never true.
Example: x + 1 = x + 4 has no solution.
Worked examples
Try the prompt first. The steps stay folded until you ask to see them.
Variables on both sides
Solve 5x − 4 = 2x + 11.
Common errors
Watch for
Only moving the variable and forgetting the sign
Subtracting 2x is not the same as dropping it.
Fix: Write the inverse operation on both sides.
Explore with an applet
Guided practice
Submit each answer to check it. The key is not shown until you do.
Question 2 of 3Both examsNY-8.EE.7Grade 8 Mathematics · Spring 2022 · Q39Non-calculatoradvanced
What value for the constant, k, will result in no solution for the equation k(5x + 7) = 10x + 12?
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Question 3 of 3Algebra I RegentsAI-A.REI.3Algebra I Regents · June 2024 · Q22Non-calculatoradvanced
When solved for x in terms of a, the solution to the equation 3x − 7 = ax + 5 is
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Intervention
Use the balance applet. Do one operation at a time and check.
Enrichment
Solve a literal equation for a specified variable, such as 2ℓ + 2w = P for w.
Explain your reasoning
Sentence starters · Notice and Wonder · Three Reads · Think-Pair-Share · Compare and Connect · Math Talk · Stronger and Clearer Each Time
- I did the same operation on both sides because…
- The variables canceled, so I looked at the remaining statement…