Solving Linear Inequalities: Key Concepts and Techniques

What are constants in an inequality?

• Numbers with a variable

• Numbers without a variable

• Letters without a number

• Letters with a number

What is the first step to solve the inequality 2x - 4 ≥ 5x + 10?

• Multiply by 5

• Add 4 to both sides

• Subtract 5x from both sides

• Divide by 2

After subtracting 5x from both sides, what is the resulting inequality?

• 3x - 4 ≥ 10

• Negative 3x + 4 ≥ 10

• Negative 3x - 4 ≥ 10

• 2x - 4 ≥ 5x + 10

What should you do after obtaining -3x - 4 ≥ 10?

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply by -3

• Divide by 3

What is the result after adding 4 to both sides of -3x - 4 ≥ 10?

• 3x ≥ 14

• -3x ≥ 14

• -3x ≥ 6

• 3x ≥ 6

What special rule must be applied when dividing by a negative number in an inequality?

• Keep the inequality sign the same

• Flip the inequality sign

• Subtract the same number from both sides

• Add the same number to both sides

What is the final solution to the inequality 2x - 4 ≥ 5x + 10?

• x ≥ 14/3

• x ≥ -14/3

• x ≤ -14/3

• x ≤ 14/3

How should the solution x ≤ -14/3 be represented on a number line?

• A closed circle at -14/3 and shading to the left

• A closed circle at -14/3 and shading to the right

• An open circle at -14/3 and shading to the right

• An open circle at -14/3 and shading to the left

What does a filled-in circle on a number line indicate?

• The inequality is not strict

• The number is not included in the solution

• The inequality is strict

• The number is included in the solution

What is the importance of making the direction of the arrow clear on a number line?

• To indicate the range of possible solutions

• To highlight the midpoint

• To mark the starting point

• To show the exact value of the solution