Solve the inequality: \(2x+5\geq13\)
- A \(x\geq3\)
- B \(x\geq4\)
- C \(x\leq4\)
- D \(x\geq9\)
Check answer and explanation
Answer B: \(x\geq4\)
Subtract \(5\): \(2x\geq8\). Divide by \(2\): \(x\geq4\).
CH05-05 lesson
Writing and Solving Inequalities Learning Activity
A focused Grade 7 learning session for Writing and Solving Inequalities using visual models, worked examples, strategy guidance, and a short mastery check.
- 18
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of writing and solving inequalities using models, equations, and test-style reasoning.
Student goal: I can solve problems involving writing and solving inequalities.
Helpful first:
Solving Multi-Step Problems with Rational Numbers
Learn the Idea
Writing and Solving Inequalities is part of Grade 7 Equations and Inequalities. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of writing and solving inequalities using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Writing and Solving Inequalities, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving writing and solving inequalities.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsWhich inequality represents "a number plus 8 is less than 15"?
- A \(x+8<15\)
- B \(x+8>15\)
- C \(x-8<15\)
- D \(8x<15\)
Check answer and explanation
Answer A: \(x+8<15\)
"A number plus 8" translates to \(x+8\), and "is less than" translates to \(<\).
guided
1 questionSolve: \(x+7<12\)
- A \(x<5\)
- B \(x>5\)
- C \(x\leq5\)
- D \(x<19\)
Check answer and explanation
Answer A: \(x<5\)
Subtract \(7\) from both sides: \(x<12-7=5\).
practice
5 questionsSolve: \(\frac{x}{3}\geq2\)
- A \(x\geq\frac{2}{3}\)
- B \(x\leq6\)
- C \(x\geq6\)
- D \(x\geq2\)
Check answer and explanation
Answer C: \(x\geq6\)
Multiply both sides by \(3\): \(x\geq6\). The inequality sign stays the same because we multiply by a positive.
Solve: \(4x<20\)
- A \(x>5\)
- B \(x<5\)
- C \(x\geq5\)
- D \(x<80\)
Check answer and explanation
Answer B: \(x<5\)
Divide both sides by \(4\): \(x<\frac{20}{4}=5\).
Solve: \(3x-4\leq11\)
- A \(x\geq5\)
- B \(x\leq5\)
- C \(x>5\)
- D \(x\leq15\)
Check answer and explanation
Answer B: \(x\leq5\)
Add \(4\): \(3x\leq15\). Divide by \(3\): \(x\leq5\).
Solve: \(-2x+3<9\)
- A \(x>-3\)
- B \(x<-3\)
- C \(x<6\)
- D \(x\geq3\)
Check answer and explanation
Answer A: \(x>-3\)
Subtract \(3\): \(-2x<6\). Divide by \(-2\) and flip the sign: \(x>-3\).
Which value of \(x\) is a solution to \(x+6>10\)?
- A \(x=3\)
- B \(x=4\)
- C \(x=5\)
- D \(x=2\)
Check answer and explanation
Answer C: \(x=5\)
Check: \(5+6=11>10\) ✓. The other values yield \(9\), \(10\), and \(8\), which do not satisfy the inequality.
exit
3 questionsMaria earns $12 per hour. How many hours must she work to earn at least $144?
- A \(h<12\)
- B \(h\geq12\)
- C \(h\leq144\)
- D \(h>12\)
Check answer and explanation
Answer B: \(h\geq12\)
"At least $144" means \(\geq\). Set up: \(12h\geq144\). Divide by \(12\): \(h\geq12\).
Which inequality represents "twice a number is at most 30"?
- A \(2x>30\)
- B \(2x\leq30\)
- C \(x\leq30\)
- D \(2x<30\)
Check answer and explanation
Answer B: \(2x\leq30\)
"Twice a number" is \(2x\); "at most" means \(\leq\).
Solve: \(\frac{x}{-4}>3\)
- A \(x<-12\)
- B \(x>-12\)
- C \(x>-\frac{3}{4}\)
- D \(x>12\)
Check answer and explanation
Answer A: \(x<-12\)
Multiply both sides by \(-4\) and flip the sign: \(x<-12\).
