Linear Equations and Literal Equations: Algebra 1 Math Test Answer Key – PDF Download

Algebra 1 Linear Test Answer Key: questions 1–5

Question 1: Variables on both sides (2 points)

Subtract \(3x\): \(2x-8=12\). Add 8: \(2x=20\). Divide: \(x=10\). Check: \(42=42\).

Scoring: 1 point for collecting variable terms and constants, 1 point for the correct solution.

Question 2: Distribute and combine (2 points)

Distribute: \(6x-3-4=5x+2\), so \(6x-7=5x+2\). Subtract \(5x\) and add 7: \(x=9\). Check: \(3(17)-4=47\) and \(5(9)+2=47\).

Scoring: 1 point for distributing and combining correctly, 1 point for the correct solution.

Question 3: Fractions on both sides (2 points)

Multiply every term by 4: \(3x+8=2x-4\). Subtract \(2x\) and 8: \(x=-12\). Check: \(-9+2=-7\) and \(-6-1=-7\).

Scoring: 1 point for clearing the denominators, 1 point for the correct solution.

Question 4: Justify each step (3 points)

Steps and reasons are shown in the figure: distribute, subtract \(2x\), add 4, divide by 2. \(x=7\). Check: \(4(6)=24\) and \(2(7)+10=24\).

Scoring: 1 point for the correct solution, 2 points for the reasons (1 point if two of the four reasons are correct).

Question 5: Solve using a graph (2 points)

1. The lines cross at \((2,3)\), so \(x=2\).
2. Add \(2x\): \(3x+1=7\); so \(3x=6\) and \(x=2\). Both sides equal 3.

Scoring: 1 point for reading the x-coordinate, 1 point for a correct algebraic check.

Algebra 1 Linear Test Answer Key: questions 6–9

Question 6: How many solutions? (2 points)

1. Right side: \(6x-4\), so \(6x-4=6x-4\) is always true: infinitely many solutions.
2. Subtract \(5x\): \(1=-3\) is false: no solution.

Scoring: 1 point for each part, including the explanation.

Question 7: Rearranging formulas (2 points)

1. \(2A=bh\), so \(b=\frac{2A}{h}\).
2. Subtract \(3x\): \(-2y=12-3x\). Divide by \(-2\): \(y=\frac{3}{2}x-6\).

Scoring: 1 point for each part.

Question 8: Text messages (3 points)

1. \(20+0.05t=27.50\)
2. Subtract 20: \(0.05t=7.50\). Divide: \(t=150\).
3. Sofia sent 150 text messages. Check: \(20+0.05(150)=27.50\).

Scoring: 1 point for a correct equation, 1 point for solving, 1 point for interpreting the answer in context.

Question 9: Garden perimeter (2 points)

1. \(2(w+w+7)=62\)
2. Simplify: \(4w+14=62\), so \(w=12\). Width 12 ft, length 19 ft.

Scoring: 1 point for the equation, 1 point for both dimensions.

Scoring summary

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