Solving one-step linear inequalities

1. Math 8 - Linear
Inequalities
Ms. Andi Fullido
© Quipper

2. Objectives
•At the end of this lesson, you
should be able to differentiate
between a linear equation and a
linear inequality in two variables.

3. Prompt
• Equations and inequalities are two of the most commonly
used terms in mathematics.
• An equation is a mathematical sentence which shows
that two quantities have the same or equal values. It uses
the equal sign “=” to show this relationship.
• An inequality, on the other hand, is a mathematical
sentence which shows that two quantities may have
different or unequal values. It uses the symbols > , < , ≥,
≤, and ≠ to show this relationship.

5. Similarities between Linear Equation and
Linear Inequality in Two Variables
•Both have two variables of degree 1.
•Both can be graphed on the
Cartesian plane.
•Their solutions can be expressed as
an ordered pair (x, y)

6. Differences between Linear Equation and
Linear Inequality in Two Variables

7. A linear equation in two variables and its
graph are shown below.
•5x+2y=14

8. A linear inequality in two variables and its
graph are shown below.
•5x+2y≥14

9. Identify whether each of the given
statements is true or false.
1. A point is a solution of a linear
equation if it is found in the shaded
area of the graph.
2. The statement y>2x−1 is a linear
inequality.
3. The statement 2x−y2=5 is a linear
equation.

11. ANSWERS
1. False; The graph of a linear equation is a
line. There is no shaded area.
2. True; This is a linear inequality written in
slope-intercept form.
3. False; A linear equation in two variables
would have exponents that are equal to 1.

12. Objectives
•At the end of this lesson, you should
be able to
•recognize the graph of a linear
inequality in two variables; and
•graph a linear inequality in two
variables.

13. Graphing Linear Inequalities in Two
Variables
• In algebra, the graph of an equation is a
representation of its solution. The solution of a
linear equation in two variables is represented by
all the points that are on its line.
• The same is true with the graph of an inequality.
The solution of a linear inequality in two variables
is represented by a shaded region, or area. This
implies that all points in the shaded area are
solutions of the inequality.

14. Graphing Linear Inequalities in Two
Variables
• Graphing a linear inequality in two variables
builds on your skill of graphing linear equations.
• The first step in the process is graphing a line
using any of the methods you've learned: slope
and y-intercept, intercepts, two points, or table of
values.
• Note the following in graphing the final line:
• If the inequality is < or >, use a broken line.
• If the inequality is ≤ or ≥, use a solid line.

15. Graphing Linear Inequalities in Two
Variables
• The next step in the process is using a test point
to determine which side to shade. A test
point can be any point on either side of the line
graph. Substitute the x and y values of the test
point to the inequality.
• Finally, if the test point is a solution, shade the
whole area where the test point is. If it is not a
solution, shade the opposite side where the test
point is.

16. How to Do
• Graph 5x+2y≥14.
• Step 1: Graph the line.
• To do this, change the inequality symbol to an equal sign.
• 5x+2y=14
• Graph using intercepts.
• Find the x-intercept.
• 5x+2y=14
5x+2(0)=14
5x=14
x=14/5≈2.8

17. How to Do
• Find the y-intercept.
• 5x+2y=14
5(0)+2y=14
2y=14
y=7
• Plot the x-intercept 2.8 on the x-axis and the y-intercept 7 on
the y-axis. Graph the line by drawing a straight line connecting
the two points.

18. How to Do
Note: The graph of the line is solid because the inequality
symbol is greater than or equal (≥).

19. How to Do
• Step 2: Determine the shaded area by using a test point.
• The easiest test point is (0,0), or the origin. Substitute x = 0 and y =
0 from the test point to the inequality.
• 5x+2y≥14
5(0)+2(0)≥14
0≥14
• Since 0 is not greater than or equal to 14, this statement is false.
This implies that the side of the line where the origin is found (left
side of the line) does not contain all the possible solutions of the
inequality.
• Instead, all the possible solutions lie on the right side of the line.

20. How to Do
• Step 3: Shade the area containing the solution

21. Graph the linear inequality 𝑦 >
2
5
𝑥 − 3 .
•Step 1: Graph the line
•Step 2: Determine the shaded area by
using a test point.
•Step 3: Shade the area containing the
solution.