Solving Linear Inequalities: Key Concepts and Techniques

What is the first step in solving the inequality 2x + 1 < 17?

• Divide both sides by 2

• Add 1 to both sides

• Subtract 1 from both sides

• Multiply both sides by 2

After subtracting 1 from both sides of the inequality 2x + 1 < 17, what is the resulting inequality?

• x < 9

• 2x < 18

• 2x < 16

• x < 8

What is the final solution to the inequality 2x + 1 < 17?

• x < 9

• x < 7

• x < 8

• x < 6

When graphing x < 8 on a number line, what type of circle should be used at 8?

• No circle

• Shaded circle

• Open circle

• Closed circle

In which direction should the arrow point when graphing x < 8 on a number line?

• Downwards

• Upwards

• To the right

• To the left

Why is it important to have the variable x on the left-hand side when graphing an inequality?

• To avoid calculation errors

• To simplify the inequality

• To ensure the arrow points in the correct direction

• To make the graph look neat

Which of the following is a method some teachers use to make the direction of the inequality clearer on a graph?

• Using a different color

• Using a thicker line

• Labeling the points

• Drawing an arrow up and over

What is another way to graph x < 8 besides using an open circle and an arrow?

• Scribbling in the direction of the inequality

• Using a dashed line

• Using a different number line

• Using a closed circle and shading

What should you remember about the circle when graphing an inequality that is not 'equal to'?

• It should be open

• It should be shaded

• It should be dashed

• It should be closed

What is the key point to remember about the direction of the arrow when graphing an inequality?

• It points upwards

• It points to the left

• It points to the right

• It points in the direction of the inequality