Correct answer: A

The correct answer is $x>5$.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Subtract 4 from both sides. Because the coefficient of x is positive, the inequality direction stays the same.
3. Check the result: The correct choice is $x>5$.

Correct answer: B

The correct answer is $x\le5$.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Divide both sides by the positive number 2, so the inequality remains x ≤ 5.
3. Check the result: The correct choice is $x\le5$.

Correct answer: C

The correct answer is $x<-4$.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Dividing by -3 reverses the inequality sign, giving x < -4.
3. Check the result: The correct choice is $x<-4$.

Correct answer: D

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

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Subtract 5 to get -2x ≥ 6, then divide by -2 and reverse the sign: x ≤ -3.
3. Check the result: The correct choice is $x\le-3$.

Correct answer: A

The correct answer is $-3<x\le3$.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Subtract 1 from all three parts to obtain -3 < x ≤ 3.
3. Check the result: The correct choice is $-3<x\le3$.

Correct answer: B

The correct answer is x = 7 or x = -7.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: A number with absolute value 7 is 7 units from zero, so both 7 and -7 are solutions.
3. Check the result: The correct choice is x = 7 or x = -7.

Correct answer: C

The correct answer is $-3<x<3$.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Numbers whose distance from zero is less than 3 lie strictly between -3 and 3.
3. Check the result: The correct choice is $-3<x<3$.

Correct answer: D

The correct answer is A closed dot at 2 with shading to the right..

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: The closed dot includes 2, and values greater than 2 are shown by shading to the right.
3. Check the result: The correct choice is A closed dot at 2 with shading to the right..

Correct answer: A

The correct answer is $x\le3$.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: Add 1 to get 4x ≤ 12, then divide by 4 to get x ≤ 3.
3. Check the result: The correct choice is $x\le3$.

Correct answer: B

The correct answer is -2.

1. Identify the algebraic structure: Determine whether the problem asks about an expression, equation, inequality, function, pattern, or model.
2. Apply the algebraic rule: The solution set contains negative numbers, and -2 is negative.
3. Check the result: The correct choice is -2.