Solving Inequalities (Solution Sets)

What does the symbol '≤' mean?

• 'greater than'

• 'less than'

• 'less than or equal to'

• 'equal to'

What does the inequality @@x + 7 ≥ 10@@ mean?

• Subtract 7 from both sides: @@x ≥ 3@@.

• Add 7 to both sides: @@x ≤ 17@@.

• Multiply both sides by 2: @@x + 14 ≥ 20@@.

• Divide both sides by 2: @@x + 3.5 ≥ 5@@.

What does the inequality @@k - 13 > -51@@ represent?

• @@k > -38@@

• @@k < -38@@

• @@k = -38@@

• @@k eq -38@@

How do you solve the inequality @@-4d - 9 ext{ ≤ } 3@@?

• Add 9 to both sides: @@-4d ext{ ≤ } 12@@, then divide by 4: @@d ext{ ≤ } -3@@.

• Add 9 to both sides: @@-4d ext{ ≤ } 12@@, then divide by -4 (remember to flip the inequality): @@d ext{ ≥ } -3@@.

• Subtract 9 from both sides: @@-4d ext{ ≥ } -6@@, then divide by -4: @@d ext{ ≤ } rac{3}{2}@@.

• Add 4 to both sides: @@-9 ext{ ≤ } 4d@@, then divide by 4: @@d ext{ ≤ } -rac{9}{4}@@.

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

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

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

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

• Strict inequalities are represented by ≤ and ≥, while non-strict inequalities are represented by < and >.

How do you represent the solution set of @@x < -4@@ on a number line?

• Draw an open circle at -4 and shade to the left.

• Draw a closed circle at -4 and shade to the right.

• Draw an open circle at -4 and shade to the right.

• Draw a closed circle at -4 and shade to the left.

What does the symbol '≥' mean?

• 'less than'

• 'greater than'

• 'greater than or equal to'

• 'equal to'

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 method of solving linear equations.

• A graphical representation of data points.

What is the graph of @@x \text{ ≥ } 4@@?

• A number line with a closed circle at 4 and shading to the right.

• A number line with an open circle at 4 and shading to the left.

• A number line with a closed circle at 4 and no shading.

• A number line with an open circle at 4 and shading to the right.

• The solution set includes all numbers less than 3.

• The solution set includes all numbers greater than 3.

• The solution set includes only the number 3.

• The solution set includes all real numbers.