7.EE.B.4: Two-step word problems

Also written as 7.EE.4

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.

In plain words: Students write and solve equations like px + q = r and p(x + q) = r, compare arithmetic and algebraic solutions, and graph and interpret solutions to two-step inequalities.

Quick picks

Common mistake: Keeping the inequality sign when dividing by a negative: −3x > 12 gives x < −4, not x > −4.
Builds on: 6.EE.B.7One-step equations 6.EE.B.8Inequalities like x > c
Leads to: 8.EE.C.7Linear equations in one variable

7.EE.B.4.aTwo-step equationsSolve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.7.EE.B.4.bTwo-step inequalitiesSolve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Khan Academy Resources

Two-step equations 7.EE.B.4.a

Two-step equations review Two-step equations Two-step equations word problems Find the mistake: two-step equations Two-step equations with decimals and fractions Equation word problem: super yoga (2 of 2)Equation word problem: super yoga (1 of 2)Two-step equation word problem: computers Two-step equation word problem: garden Two-step equations with decimals and fractions Worked example: two-step equations Two-step equations intuition Intro to two-step equations Two-step equation word problem: oranges Two-step equations with decimals and fractions Find the mistake: two-step equations

Two-step inequalities 7.EE.B.4.b

One-step inequalities review One-step inequalities Two-step inequalities Two-step inequality word problems One-step inequalities: -5c ≤ 15 One-step inequalities examples Two-step inequality word problem: apples Two-step inequalities One-step inequality word problem Two-step inequality word problem: R&B

Two-step word problems 7.EE.B.4

Testing solutions to inequalities

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