Solving Inequalities

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 data points on a coordinate plane.

• A method for solving linear equations.

What does the symbol '≤' mean?

• 'greater than'

• 'less than'

• 'less than or equal to'

• 'equal to'

What is a solution set in the context of inequalities?

• A solution set is the set of all values that satisfy the inequality.

• A solution set is a graphical representation of the inequality.

• A solution set is the range of values that do not satisfy the inequality.

• A solution set is a single value that solves the inequality.

What does the symbol '≥' mean?

• 'less than'

• 'greater than'

• 'greater than or equal to'

• 'equal to'

What does it mean to 'solve and graph' an inequality?

• To find the solution set and represent it visually on a number line.

• To calculate the roots of the inequality only.

• To express the inequality in standard form without graphing.

• To determine the maximum and minimum values of the inequality.

What is the solution to the inequality s + 9 ≥ -25?

• s ≥ -34

• s ≥ -25

• s ≤ -34

• s ≤ -25

How do you solve the inequality -3x ≤ 18?

• Divide both sides by -3, remembering to flip the inequality sign: x ≥ -6.

• Add 3 to both sides: x ≤ 21.

• Multiply both sides by -3: x ≤ -6.

• Subtract 18 from both sides: -3x - 18 ≤ 0.

How do you check if a number is a solution to an inequality?

• Substitute the number into the inequality and see if the statement is true.

• Graph the inequality and see if the number lies in the shaded region.

• Calculate the absolute value of the number and compare it to the inequality.

• Use the number to create a new inequality and solve for a variable.

How do you solve the inequality x - 7 ≥ 4?

• Add 7 to both sides: x ≥ 11.

• Subtract 7 from both sides: x ≥ -3.

• Multiply both sides by -1: x ≤ -11.

• Divide both sides by 2: x ≥ 2.

How do you graph the inequality x ≥ -6?

• Draw a number line, place a closed circle on -6, and shade to the right.

• Draw a number line, place an open circle on -6, and shade to the left.

• Draw a number line, place a closed circle on -6, and shade to the left.

• Draw a number line, place an open circle on -6, and shade to the right.