Maryland Math 8.AT.B.4.a

Math8th GradeAlgebraic Thinking

The Standard

Solve inequalities including those requiring the use of the distributive property and combining like terms.

Maryland College and Career Ready Standards for Mathematics (2025) · MAKE SENSE OF AND SOLVE EQUATIONS, INEQUALITIES, AND SYSTEMS OF EQUATIONS.

Teacher's field guide

What Students Need to Do: Students expand parentheses, combine like terms, and solve inequalities with one variable. They reverse the inequality sign when dividing by a negative number and describe all values that work.
What Mastery Looks Like: Given 2(x + 3) - 4x ≤ 10, a student gets x ≥ -2 and marks -2 with a closed dot on a number line. They test x = 0 in the original inequality to check their answer.
Common Misconceptions: Students may distribute a negative number to only one term inside the parentheses. They may forget to reverse the inequality sign when dividing by a negative number, or give one number instead of all values that work.
How to Assess It: Solve 6 - 2(x + 3) ≥ 4 - x. Show your steps, then check x = -5 and x = 0 in the original inequality.

Lesson moves

Use algebra tiles to build 2(x + 3) - x > 7, expand the groups, and remove tiles to find x > 1.
Ask, “Why does dividing -4x < 12 by -4 change the inequality sign?” Have students test x = -4 and x = 0.
Match cards for 2(x + 1) > 8, -2(x + 3) ≥ 4, and 5 - x < 1 with solved inequalities.
A club has $50 for three $x snack bags, each with $2 wrapping, and $5 delivery; solve 3(x + 2) + 5 ≤ 50.

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