Two-Step Equations: Grade 7 Math Test Answer Key – PDF Download

Question 1: Add, then multiply (2 points)

\(6x=36\), so \(x=6\). Check: \(6(6)+9=45\).

Scoring: 1 point for subtracting 9 correctly, 1 point for dividing by 6.

Question 2: Fraction of a variable (2 points)

Add 4: \(\frac{x}{3}=9\). Multiply by 3: \(x=27\). Check: \(\frac{27}{3}-4=5\).

Scoring: 1 point for \(\frac{x}{3}=9\), 1 point for \(x=27\).

Question 3: Negative coefficient (2 points)

Subtract 7: \(-2x=-12\). Divide by \(-2\): \(x=6\). Check: \(-2(6)+7=-5\). The graph is a point at 6.

Scoring: 1 point for \(-2x=-12\), 1 point for \(x=6\) correctly graphed.

Question 4: Parentheses (2 points)

Divide by 3: \(x-5=7\). Add 5: \(x=12\). Check: \(3(12-5)=3(7)=21\).

Scoring: 1 point for a correct first step (\(x-5=7\) or \(3x-15=21\)), 1 point for \(x=12\).

Question 5: Decimal coefficients (2 points)

Subtract 2.25: \(1.5x=7.5\). Divide by 1.5: \(x=5\). Check: \(1.5(5)+2.25=7.5+2.25=9.75\).

Scoring: 1 point for \(1.5x=7.5\), 1 point for \(x=5\).

Question 6: Fraction coefficient (2 points)

Add 4: \(\frac{2}{3}x=10\). Multiply by \(\frac{3}{2}\): \(x=10\cdot\frac{3}{2}=15\). Answer: \(x=15\). Check: \(\frac{2}{3}(15)-4=10-4=6\).

Scoring: 1 point for \(\frac{2}{3}x=10\), 1 point for \(x=15\).

Question 7: Find the error (2 points)

Liam added 6 to both sides, but the equation has \(+6\), so he must subtract 6: \(4x=30-6=24\). Then \(x=6\). Check: \(4(6)+6=30\), while \(4(9)+6=42\).

Scoring: 1 point for explaining that 6 must be subtracted, 1 point for \(x=6\).

Question 8: School store receipt (3 points)

(a) \(4n+3.50=17.50\).

(b) Subtract 3.50: \(4n=14\). Divide by 4: \(n=3.50\). A notebook costs \(\$3.50\).

(c) \(4(3.50)+3.50=14+3.50=17.50\). It checks.

Scoring: 1 point per part.

Question 9: Two ways to find a number (3 points)

(a) \(4(x+7)=52\).

(b) Divide by 4: \(x+7=13\). Subtract 7: \(x=6\).

(c) Work backward: \(52: 4=13\), then \(13-7=6\). These are the same two operations as in the algebra, in the same order. Check: \((6+7)\cdot 4=52\).

Scoring: 1 point per part. In (c), the explanation must mention the same inverse operations.

⬇ Download the Grade 7 Two-Step Equations test answer key (PDF, 97 KB)

See every chapter on the Grade 7 math page.