Understanding and Solving Inequalities

What is the key difference between solving equations and inequalities?

• You must always multiply both sides by a positive number.

• You must always subtract a constant from both sides.

• You must flip the inequality sign when multiplying or dividing by a negative number.

• You must always add a constant to both sides.

When graphing the inequality x > 3 on a number line, what type of circle should be used at 3?

• An open circle, because 3 is included.

• A closed circle, because 3 is not included.

• A closed circle, because 3 is included.

• An open circle, because 3 is not included.

If you have the inequality x - 5 > 10, what is the first step to solve for x?

• Add 5 to both sides.

• Subtract 5 from both sides.

• Multiply both sides by 5.

• Divide both sides by 5.

In the inequality -3x < 9, what must you do after dividing both sides by -3?

• Flip the inequality sign.

• Keep the inequality sign the same.

• Subtract 3 from both sides.

• Add 3 to both sides.

How do you handle a fractional coefficient when solving an inequality?

• Subtract the reciprocal from both sides.

• Add the reciprocal to both sides.

• Multiply by the reciprocal.

• Divide by the reciprocal.

What is the solution to the inequality 2x + 3 ≤ 7?

• x ≤ 2

• x ≤ 5

• x ≥ 2

• x ≥ 5

When graphing x ≤ -4, which direction should you shade on the number line?

• Shade both sides of -4.

• Shade to the right of -4.

• Shade to the left of -4.

• Do not shade at all.

If you have the inequality 4y > -20, what is the value of y?

• y < -5

• y > -5

• y < 5

• y > 5

In a real-world scenario, if you have $50 and each item costs $8 with a $2 delivery fee, what is the maximum number of items you can buy?

• 8 items

• 7 items

• 6 items

• 5 items

What inequality represents the scenario where you have $40 to spend, with a $5 delivery fee and each item costing $7?

• 5x + 7 ≤ 40

• 5x + 7 ≥ 40

• 5 + 7x ≥ 40

• 5 + 7x ≤ 40