Graphing and Solving Linear Inequalities Challenge

What is the main difference between a linear equation and a linear inequality?

• A linear equation can only have one solution, while a linear inequality can have multiple solutions.

• A linear equation has a variable, while a linear inequality does not.

• A linear equation uses an equal sign, while a linear inequality uses inequality signs.

• A linear equation is always graphed as a straight line, while a linear inequality is graphed as a curve.

When graphing x > -2 on a number line, what type of circle should be used at -2?

• Closed circle

• Open circle

• No circle

• Half-filled circle

If you have the inequality x ≤ 110, how should you represent this on a number line?

• Open circle at 110 and shade to the right

• Closed circle at 110 and shade to the left

• Closed circle at 110 and shade to the right

• Open circle at 110 and shade to the left

What must you remember to do when you multiply or divide both sides of an inequality by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Reverse the inequality sign

• Keep the inequality sign the same

In the inequality 8k - 3 > -24, what is the first step to solve for k?

• Divide both sides by 8

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 8

When graphing a linear inequality in two variables, what is the first step?

• Determine which side to shade

• Draw a dashed line

• Find the x and y intercepts

• Test a point not on the boundary line

How do you determine if the boundary line should be dashed or solid?

• If the inequality includes 'equal to', use a solid line; otherwise, use a dashed line.

• Always use a solid line.

• If the inequality includes 'greater than', use a solid line; otherwise, use a dashed line.

• Always use a dashed line.

What is the purpose of testing a point when graphing a linear inequality in two variables?

• To determine which side of the boundary line to shade

• To check if the point lies on the boundary line

• To find the slope of the line

• To determine the x-intercept

If you test the point (0,0) in the inequality 3x - y ≤ 6 and find it true, what does this mean?

• The point (0,0) is not a solution to the inequality.

• The side of the boundary line not containing (0,0) is the true side.

• The point (0,0) lies on the boundary line.

• The side of the boundary line containing (0,0) is the true side.

When graphing the inequality y > 2x - 3, which side of the boundary line should be shaded?

• Above the line

• Below the line

• On the line

• None of the above