Grade 7 Inequalities Practice Test

Correct answer: A

The correct answer is An open circle at 3, shaded to the right.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: The symbol > excludes 3, so use an open circle, and values greater than 3 lie to the right.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: B

The correct answer is A closed circle at -2, shaded to the left.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: The symbol \le includes -2, so use a closed circle, and smaller values lie to the left.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: C

The correct answer is $x\ge4$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: Subtract 1: $2x\ge8$. Divide by 2: $x\ge4$.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: D

The correct answer is $x<5$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: An open circle excludes 5, and shading left represents values less than 5.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: A

The correct answer is $-2<x\le4$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: Greater than -2 is $-2<x$, and at most 4 is $x\le4$.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: B

The correct answer is $x\le7$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: A closed circle includes 7, and shading left means values less than or equal to 7.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: C

The correct answer is $x\ge-3$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: A closed circle includes -3, and shading right represents values greater than or equal to -3.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: D

The correct answer is $x<2\text{ or }x\ge6$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: The two separate intervals are $x<2$ and $x\ge6$, joined by or.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: A

The correct answer is $x<4$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: Add 2: $3x<12$. Divide by 3: $x<4$.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.

Correct answer: B

The correct answer is $x\le-3$.

1. Isolate the variable: Use inverse operations to move constants and coefficients while preserving the inequality.
2. Apply the inequality rule: Subtract 5: $-2x\ge6$. Divide by -2 and reverse the sign: $x\le-3$.
3. Check the solution: Test a value from the solution set and confirm that it satisfies the original inequality.