Solving Inequalities

What does the inequality x ≥ -5 represent on a number line?

• All numbers less than -5

• All numbers greater than -5

• All numbers greater than or equal to -5

• All numbers equal to -5

What does the symbol '≤' mean?

• 'greater than'

• 'less than'

• 'less than or equal to'

• 'equal to'

Solve the inequality 5z - 2 - 2z < 13.

• z < 3

• z < 4

• z < 5

• z < 6

What does the symbol '≥' mean?

• 'less than'

• 'greater than'

• 'greater than or equal to'

• 'equal to'

What is the first step in solving the inequality 8y < -40?

• Add 40 to both sides to isolate y.

• Multiply both sides by 8 to isolate y.

• Divide both sides by 8 to isolate y.

• Subtract 8 from both sides to isolate y.

How do you solve the inequality -4x + 14 ≤ 54?

• x ≥ -10.

• x ≤ -10.

• x > -10.

• x < -10.

What is an inequality?

• A mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

• A type of equation that shows equality between two expressions.

• A graphical representation of a function.

• A method for solving linear equations.

When solving inequalities, does the sign flip when multiplying or dividing by a negative number?

• No, the sign does not flip.

• Yes, the sign flips when multiplying or dividing by a negative number.

• The sign flips only when dividing by a negative number.

• The sign flips only when multiplying by a negative number.

What is the difference between strict and non-strict inequalities?

• Strict inequalities include the endpoint, while non-strict inequalities do not.

• Strict inequalities do not include the endpoint, while non-strict inequalities do.

• Strict inequalities are always greater than, while non-strict inequalities can be equal.

• Strict inequalities are used only in calculus, while non-strict inequalities are used in algebra.

How do you graph the inequality x < 3 on a number line?

• Draw an open circle at 3 and shade to the left.

• Draw a closed circle at 3 and shade to the right.

• Draw an open circle at 3 and shade to the right.

• Draw a closed circle at 3 and shade to the left.