7.11.A
The Standard
model and solve one-variable, two-step equations and inequalities
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a situation or model into an algebraic statement with one unknown. They use inverse operations to isolate the variable, then check or graph the result.
What Mastery Looks Like
- Students can build an equation or inequality from a short situation, diagram, or model. They solve while keeping both sides balanced, check equations by substitution, and graph inequality solutions with the correct endpoint.
Common Misconceptions
- Students may undo operations in the wrong order or change only one side. They often forget to reverse the inequality sign after multiplying or dividing by a negative number. Some give one value instead of a range of solutions.
How to Assess It
- Give this exit ticket: Solve 4x - 7 = 21. Then write, solve, and graph an inequality for: $5 admission plus $3 per ride costs at most $20.
Lesson moves
Ways to Teach It
Use algebra tiles on balance mats to represent 2x + 3 = 15, then remove tiles and split the remaining tiles equally.
Ask students to explain why dividing both sides by a negative number reverses an inequality sign, using two number-line examples.
Run a card sort matching each situation with its equation or inequality, solution, and number-line graph.
Have students write and solve an inequality for staying within a budget that includes a fixed fee and a cost per item.
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Printable 7.11.A Worksheet
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Related Standards
- 6.9.B
represent solutions for one-variable, one-step equations and inequalities on number lines
- 6.10.A
model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts
- 7.10.C
write a corresponding real-world problem given a one-variable, two-step equation or inequality
- 7.10.B
represent solutions for one-variable, two-step equations and inequalities on number lines
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