Review of Solving Linear Inequalities

Linear Inequality Review

Review Day 2

Multiple Choice

Solve the inequality y > 3x + 2

if x = 7

• y > 12

• y < 12

• y > 23

• y < 23

Multiple Choice

Here is the inequality $$4\ <\ 3x\ +\ 2$$  is x = 0 a solution?

• Yes, the solution is less than 4

• Yes, the solution is greater than 4

• No, the solution is less than 4

• No, the solution is greater than 4

​Solving Inequalities

​Just like with linear equations, to solve for one inequality, we need to isolate the variable.

​

​*Note: If you divide by a negative number, the inequality symbol changes directions

​Example: 6x -3y > 15

Multiple Choice

Solve the inequality 3x - 2 > 5x + 10

• -6 > x

• -6 < x

• 8 > x

• 8 < x

Open Ended

Here is the inequality $$y\ \ +\ 3x\ \ge\ 4y\ +\ 2x\ +10$$  

Solve for y.

​Graphing an Inequalities on a number line

Let's graph the solution to y + 2 > 7

Draw

Use the number line to graph the solution to $$3+x\ge7$$  

Draw

Use the number line to graph the solution to -4x + 8 < 12

​Graphing Inequalities

​Set up the inequality like we would     y = mx + b where “ y ” is all alone.

1. Graph the line (same as a linear equation)

2. Plot the points on a graph and connect the dots.

3. Make the line dotted or straight based on the inequality symbol

   1. < or >  use  dotted

   2. ≤ or ≥  use straight

4. Determine which side of the line will be shaded by plugging in random points on either side and seeing which ones make the inequality true

​y + 3 > x + 1

Draw

Graph $$7y\ge\ 14x\ -\ 28$$  

​Solution for a System of Inqualities

1. ​Solutions to a system make BOTH equations true

2. ​If the inequalites are given, find a point in the overlapping region and plug the value into both equations

   1. ​If both are true, then that region is where the solutions are

   2. ​If only one is true, that is NOT a solution to the system

   3. ​If both are not true, that is NOT a solution to the system

Multiple Choice

Which graph shows the solution to the system:

$$3x\ +\ 7y\ <21$$  

$$y\ \ge2x\ -4$$  

Multiple Choice

Here is a system of inequalities:

$$x\ +\ y\ <\ 3$$  

$$y\ \ge\ x\ -\ 4$$  

Is the point (2, -6) a solution to the system?

• Yes, it is in the overlapping section

• No, it is only a solution to x + y < 3

• No, it is only a solution to $$y\ \ge\ x-4$$  

• No, it is a solution to neither

Open Ended

Here is a system of inequalities:

$$x\ +\ y\ <\ 3$$  

$$y\ \ge\ x\ -\ 4$$  

List a coordinate pair that could be a solution to the system.