Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Many everyday questions turn into equations with two steps. A gym charges a $25 sign-up fee plus $15 per month, and Kim has paid $130 in total: how many months has she been a member? Writing 15m + 25 = 130 and solving it is exactly the kind of work seventh graders learn here, with equations of the forms px + q = r and p(x + q) = r, where p, q and r can be any rational numbers.
Students solve these fluently by undoing operations in reverse order, and they also compare the algebraic method to an arithmetic one (subtract the fee, then divide by the monthly cost), noticing that both use the same operations in the same sequence. The standard then extends to inequalities such as 120 + 20w ≥ 280. Students solve them, graph the solution set on a number line and interpret it in context, for example deciding that the solutions must be whole numbers of weeks. A key subtlety is that multiplying or dividing both sides by a negative number reverses the inequality sign.
In 4x + 7 = 31, dividing by 4 first gives x + 7 = 7.75, which is wrong because the 7 was not multiplied by 4. Undo addition and subtraction before multiplication and division.
Solving -2x + 5 > 13 by dividing by -2 without reversing the sign gives x > -4. Testing a value such as x = 0 shows it does not work, so the solution must be x < -4.
3(x - 2) = 18 must become 3x - 6 = 18. Some students write 3x - 2 = 18. Dividing both sides by 3 first, x - 2 = 6, avoids the issue.
If w is a number of weeks, the answer w ≥ 8 means 8, 9, 10 and so on, not 8.5. Ask students which values on the graph make sense.
A gym charges a $25 sign-up fee plus $15 per month. Kim has paid $130 in total. How many months has she been a member?
Answer: Kim has been a member for 7 months.
Bar models are a strong bridge from arithmetic to algebra: draw 15m + 25 as fifteen-dollar blocks plus a fee block, totaling 130. Students who can solve the bar model can usually explain each line of the algebra, which is what the standard means by comparing solutions.
For inequalities, start with situations where students can reason about 'at least' and 'at most' before introducing symbols, and always ask them to test one value from their solution set. Test items often include writing the inequality from a story, solving it and choosing the matching number-line graph.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 6 (also accepted: x = 6, x=6)
Subtract 7 from both sides: 4x = 24. Divide by 4: x = 6.
Answer: 8 (also accepted: x = 8, x=8)
Divide both sides by 3: x - 2 = 6. Add 2: x = 8.
Answer: B) 8 cm
2(15) + 2w = 46, so 30 + 2w = 46. Subtract 30: 2w = 16. Divide by 2: w = 8 cm.
Answer: C) 120 + 20w ≥ 280
Her savings after w weeks are 120 + 20w, and 'at least $280' means greater than or equal to 280. Solving gives w ≥ 8 weeks.
Answer: x < -4 (also accepted: x<-4, -4 > x)
Subtract 5: -2x > 8. Divide by -2 and reverse the sign: x < -4. Check x = -5: -2(-5) + 5 = 15, which is greater than 13.
Answer: A) 16
Add 3 to both sides: (1/2)x = 8. Multiply both sides by 2: x = 16.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A full lesson with slides, activities and an exit ticket on two-step equations and inequalities, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.EE.B.4 with an answer key, ready in about a minute.
Make a worksheet →Turn two-step equations and inequalities into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Equations of the form px + q = r and p(x + q) = r, and inequalities of the form px + q > r or px + q < r, where p, q and r are rational numbers.
Multiplying or dividing by a negative reverses the order of numbers: 2 < 3 but -2 > -3. To keep the statement true, the sign must reverse too.