Graphing Inequalities on a Number Line

The video tutorial covers graphing inequalities, explaining how they differ from equations by using inequality signs instead of equal signs. It demonstrates solving inequalities by isolating variables and graphing solutions on a number line. The tutorial includes examples with positive and negative coefficients, emphasizing the need to flip inequality signs when multiplying or dividing by negatives. It also addresses common confusions, such as handling zero in inequalities.

What symbol is used in inequalities instead of an equal sign?

• Plus sign

• Multiplication sign

• Greater than or less than sign

• Percentage sign

When graphing x > 1, how is the number 1 represented on the graph?

• With a filled dot

• With an open dot

• With a triangle

• With a square

What is the correct graph representation when x is less than or equal to 11?

• Shade to the left of 11

• Shade to the right of 11

• No shading at all

• Only a dot at 11

How do you solve an inequality with a fractional coefficient for x?

• Divide by the numerator

• Subtract the numerator from both sides

• Multiply by the reciprocal of the fraction

• Add the denominator to both sides

What must be done when dividing both sides of an inequality by a negative number?

• Add a zero to both sides

• Multiply by -1

• Keep the inequality sign the same

• Flip the inequality sign

In the inequality -4x ≤ 8, what is the value of x after solving?

• x ≥ 2

• x ≤ 2

• x ≤ -2

• x ≥ -2

What is the correct representation on a graph for x ≤ -9?

• Open circle at -9 and shade to the left

• Filled circle at -9 and shade to the left

• Open circle at -9 and shade to the right

• Filled circle at -9 and shade to the right

How is the number zero treated in inequalities?

• Just like any other number

• As an undefined number

• As a positive number

• As a negative number

What is the solution to the inequality 2x < 8?

• x < 4

• x > 3

• x < 3

• x > 4

When graphing the solution to an inequality, what does an open circle represent?

• That the number is not included in the solution

• That the solution is zero at that number

• That the number is included in the solution

• That the solution is undefined at that number