Solving Linear Inequalities with One Variable

What is the first step in solving the inequality x - 4 > 3?

• Subtract 4 from both sides

• Divide both sides by 4

• Add 4 to both sides

• Multiply both sides by 4

How do you represent the solution x > 7 on a number line?

• A closed circle at 7 and shading to the right

• An open circle at 7 and shading to the right

• An open circle at 7 and shading to the left

• A closed circle at 7 and shading to the left

What is the solution to the inequality 3x + 2 ≤ 8?

• x ≤ 2

• x < 2

• x > 2

• x ≥ 2

When solving 2x - 1 < 3x + 5, what is the resulting inequality after isolating x?

• x > -6

• x < 6

• x > 6

• x < -6

What happens to the inequality sign when you multiply or divide both sides by a negative number?

• It stays the same

• It becomes an equal sign

• It disappears

• It reverses direction

What does it mean if you end up with a true statement like 0 ≤ 2 when solving an inequality?

• The solution is zero

• There is one solution

• There are infinite solutions

• There is no solution

What does it mean if you end up with a false statement like -1 > 4 when solving an inequality?

• There are infinite solutions

• The solution is zero

• There is one solution

• There is no solution

In the compound inequality 0 < x ≤ 2, how is it represented on a number line?

• Open circle at 0, closed circle at 2, shading in between

• Closed circle at 0, open circle at 2, shading in between

• Open circle at 0, open circle at 2, shading in between

• Closed circle at 0, closed circle at 2, shading in between

What is the solution to the inequality x - 3 ≤ -6?

• x ≤ 3

• x ≥ -3

• x ≤ -3

• x ≥ 3

In the compound inequality x < -1 or x ≥ 3, how is it represented on a number line?

• Closed circle at -1, open circle at 3, shading outside

• Closed circle at -1, open circle at 3, shading in between

• Open circle at -1, closed circle at 3, shading outside

• Open circle at -1, closed circle at 3, shading in between