Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
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
Before students learn methods for solving, sixth grade frames solving as answering a question: which values, from a given set, make this equation or inequality true? For x + 7 = 12, the question is which number added to 7 gives 12. For 3n > 15, it is which numbers, when tripled, give more than 15. The answer might be one value, several values or none at all.
Substitution is the tool. Students replace the variable with each candidate number and check whether the resulting statement is true. Given the set {2, 4, 6, 8} and the inequality 2x + 1 < 12, they test each: 5, 9 and 13 come out below 12 for x = 2 and 4, but x = 6 gives 13, so only 2 and 4 work. This idea, that a solution is a value making a statement true, carries all the way through algebra, and it also gives students a dependable way to check any answer they find later by other methods.
Students sometimes pick a number that appears in the equation, such as 7 in x + 7 = 12. Substituting 7 gives 14, which shows it is not a solution.
For 3n > 15, n = 5 gives 15 > 15, which is false. Students must read the inequality symbol carefully, including whether the boundary is included.
With an inequality and a set of candidates, more than one value can work. Students should test every value in the set.
Which values in the set {3, 5, 7, 9} are solutions of 4x - 6 ≥ 20?
Answer: 7 and 9 are solutions; 3 and 5 are not.
Present solving as a guessing-and-checking game first, using small sets, before introducing inverse operations in 6.EE.B.7. Asking students to explain why a value fails is as valuable as finding the ones that work.
Assessment items often give a set of numbers and an equation or inequality and ask for all solutions, or ask whether a given value is a solution. Fractions and decimals in the set are common.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) 14
Substitute: 14 + 9 = 23. True. The others give 18, 32 and 41.
Answer: C) No, because 30 < 30 is false
5 × 6 = 30, and 30 < 30 is false. 30 is not less than itself.
Answer: 3
Test: 3(3) - 2 = 9 - 2 = 7. True. The others give 1, 4 and 10.
Answer: 3
2y gives 4, 8, 12, 16 and 20. Only 12, 16 and 20 are greater than 11, so 3 values (6, 8 and 10) work.
Answer: B) 4x = 2
4 × 1/2 = 2, so 4x = 2 is true when x = 1/2.
A full lesson with slides, activities and an exit ticket on solutions of equations and inequalities, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.EE.B.5 with an answer key, ready in about a minute.
Make a worksheet →Turn solutions of equations and inequalities into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Finding which values from a given set, if any, make an equation or inequality true. Students check each value by substitution.
Yes. If none of the values in the set make the statement true, the answer is that there is no solution in that set.