Testinar Grade 7 math

Solving Equations with the Distributive Property

Students will build Grade 7 mastery of solving equations with the distributive property using models, equations, and test-style reasoning.

CH05-03 Equations and Inequalities

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Solve for \(x\): \(3(x+4)=27\)
1. \(x=5\)
2. \(x=7\)
3. \(x=9\)
4. \(x=23\)
Solve for \(x\): \(5(x-2)=35\)
1. \(x=5\)
2. \(x=7\)
3. \(x=9\)
4. \(x=12\)
Solve for \(x\): \(2(x+6)=20\)
1. \(x=2\)
2. \(x=4\)
3. \(x=6\)
4. \(x=8\)
Solve for \(x\): \(4(x-3)=12\)
1. \(x=0\)
2. \(x=3\)
3. \(x=6\)
4. \(x=9\)
Solve for \(x\): \(6(x+2)=30\)
1. \(x=1\)
2. \(x=3\)
3. \(x=5\)
4. \(x=7\)
Solve for \(x\): \(2(x-5)=14\)
1. \(x=7\)
2. \(x=12\)
3. \(x=9\)
4. \(x=5\)
Solve for \(x\): \(7(x+1)=49\)
1. \(x=5\)
2. \(x=6\)
3. \(x=7\)
4. \(x=8\)
Solve for \(x\): \(-3(x-2)=15\)
1. \(x=-3\)
2. \(x=-1\)
3. \(x=3\)
4. \(x=7\)

Teacher and parent reference

Answer key and explanations

A. \(x=5\)
Distribute: \(3x+12=27\). Subtract \(12\): \(3x=15\). Divide by \(3\): \(x=5\). (Distractor D: forgetting to distribute gives \(x+4=27 \Rightarrow x=23\).)
C. \(x=9\)
Distribute: \(5x-10=35\). Add \(10\): \(5x=45\). Divide by \(5\): \(x=9\). (Distractor A: solving \(x-2=5\) instead; Distractor D: arithmetic error when isolating \(x\).)
B. \(x=4\)
Distribute: \(2x+12=20\). Subtract \(12\): \(2x=8\). Divide by \(2\): \(x=4\). (Distractor A: dividing only the right side; Distractor C: forgetting to divide by 2; Distractor D: arithmetic error in final step.)
C. \(x=6\)
Distribute: \(4x-12=12\). Add \(12\): \(4x=24\). Divide by \(4\): \(x=6\).
B. \(x=3\)
Distribute: \(6x+12=30\). Subtract \(12\): \(6x=18\). Divide by \(6\): \(x=3\).
B. \(x=12\)
Distribute: \(2x-10=14\). Add \(10\): \(2x=24\). Divide by \(2\): \(x=12\).
B. \(x=6\)
Distribute: \(7x+7=49\). Subtract \(7\): \(7x=42\). Divide by \(7\): \(x=6\).
A. \(x=-3\)
Distribute: \(-3x+6=15\). Subtract \(6\): \(-3x=9\). Divide by \(-3\): \(x=-3\).