Florida Grade 6 Math · Algebraic Reasoning

MA.6.AR.2.1: Testing Values in Equations and Inequalities

What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.

Created by a Florida mom · Published by Tropical Learning LLC

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What Is Benchmark MA.6.AR.2.1?

Given an equation or inequality and a set of integer values, students decide which values make it true. The variable may appear in more than one term or on either side.

Substitute each value and check whether the statement is true. For inequalities, more than one value can work.

Official benchmarkGiven an equation or inequality and a specified set of integer values, determine which values make the equation or inequality true or false.

On the FAST test: part of the Grade 6 reporting category Algebraic Reasoning, which is about 25–36% of the test.

Worked Examples

Worked Example 1

An Inequality

Which of −1, 2, 3, and 5 make 2x − 3 > 1 true?

1x = −1: 2 × (−1) − 3 = −5, and −5 is not greater than 1.
2x = 2: 2 × 2 − 3 = 1, and 1 is not greater than 1.
3x = 3: 2 × 3 − 3 = 3 > 1. x = 5: 2 × 5 − 3 = 7 > 1.

Answer: 3 and 5

Worked Example 2

Variable on Both Sides

Which of −3, −1, and 2 make 3n + 4 = n − 2 true?

1n = −3: 3 × (−3) + 4 = −5 and −3 − 2 = −5, so both sides match.
2n = −1: 3 × (−1) + 4 = 1 and −1 − 2 = −3, so the sides don't match.
3n = 2: 3 × 2 + 4 = 10 and 2 − 2 = 0, so the sides don't match.

Answer: −3

Common Mistakes to Watch For

Treating > as ≥

Wrong:x = 2 works for 2x − 3 > 1, because it gives 1.

1 > 1 is not true. With >, the two sides can't be equal.

Losing the negative sign when substituting

Wrong:For x = −3, 2x = 6.

2 × (−3) = −6. Write negative values in parentheses.

Helpful Math Tip

Make a small table with a column for each value, the left side, the right side, and "true?" It keeps the work organized.

Related Grade 6 Skills

MA.6.AR.1.2

Writing and Graphing Inequalities

MA.6.AR.1.3

Evaluating Expressions

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Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.