inequalities. symbolmeaning greater than =equal greater than or equal to. ...
TRANSCRIPT
GRAPHING SOLUTIONSInequalities
Inequality Symbols
Symbol Meaning
< Less Than
> Greater Than
= Equal
< Less Than or Equal To
> Greater Than or Equal To
What You Need
A number line ex:
A variable ex: x, y, v, z, etc.
To Shade ex: Shade all solutions that make the inequality true!
Do NOT shade the direction of the sign! Instead, only shade where the solutions are
true.
x < 5 Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 < 5 This is false, so 5 does not work.
Does 6 work? Substitute 6 for the variable and check. 6 < 5. This is false, so 6 does not work.
Does 4 work? Substitute 4 for the variable and check. 4 < 5. This is true, so 4 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. 4 is a value that works & is located on the left of 5 on the number line. Shade
on the left.
5
5 > x Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 < 5 This is false, so 5 does not work.
Does 6 work? Substitute 6 for the variable and check. 5 > 6. This is false, so 6 does not work.
Does 4 work? Substitute 4 for the variable and check. 5 > 4. This is true, so 4 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. 4 is a value that works & is located on the left of 5 on the number line. Shade
on the left.
5
NOTICE!!!
x < 5 has the same graph as 5 > x!
Although the signs point in different directions, for these inequalities,
the solutions that make the inequalities true are on the left of 5 on the number
line.
AGAIN…. WARNING!
Do NOT shade the direction of the sign!
Instead, only shade the side where the solutions are true.
> does not always mean shade on the right!< does not always means shade on the left!
x > 5 Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 > 5 This is false, so 5 does not work.
Does 4 work? Substitute 4 for the variable and check. 4 > 5. This is false, so 4 does not work.
Does 6 work? Substitute 6 for the variable and check. 6 > 5. This is true, so 6 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. 6 is a value that works & is located on the right of 5 on the number line. Shade
on the right.
5
5 < x Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 < 5 This is false, so 5 does not work.
Does 4 work? Substitute 4 for the variable and check. 5 < 4. This is false, so 4 does not work.
Does 6 work? Substitute 6 for the variable and check. 5 < 6. This is true, so 6 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. 6 is a value that works & is located on the right of 5 on the number line. Shade
on the right.
5
NOTICE!!!
x > 5 has the same graph as 5 < x!
Although the signs point in different directions, for these inequalities, the solutions that make it true are on the
right of 5 on the number line.
AGAIN…. WARNING!
Do NOT shade the direction of the sign!
Instead, only shade the side where the solutions are true.
> does not always mean shade on the right!< does not always means shade on the left!
x < 5 Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 < 5 This is true, so 5 does work.
Does 6 work? Substitute 6 for the variable and check. 6 < 5. This is false, so 6 does not work.
Does 4 work? Substitute 4 for the variable and check. 4 < 5. This is true, so 4 does work !
Step 2: Draw a number line and the shade where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! 4 is a value that works & is located on the left of 5 on the number line. Shade
on the left.
5
5 > x Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 > 5 This is true, so 5 does work.
Does 6 work? Substitute 6 for the variable and check. 5 > 6. This is false, so 6 does not work.
Does 4 work? Substitute 4 for the variable and check. 5 > 4. This is true, so 4 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! 4 is a value that works & is located on the left of 5 on the number line. Shade
on the left. 5
NOTICE!!!
x < 5 has the same graph as 5 > x!
Although the signs point in different directions, for these inequalities, the solutions that make it true are on the
left of 5 on the number line.
AGAIN…. WARNING!
Do NOT shade the direction of the sign!
Instead, only shade the side where the solutions are true.
> does not always mean shade on the right!< does not always means shade on the left!
x > 5 Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 > 5 This is true, so 5 does work.
Does 4 work? Substitute 4 for the variable and check. 4 > 5. This is false, so 4 does not work.
Does 6 work? Substitute 6 for the variable and check. 6 > 5. This is true, so 6 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! 6 is a value that works & is located on the right of 5 on the number line. Shade
on the right. 5
5 < x Step 1: Determine a solution that makes the inequality
true.
Does 5 work? Substitute 5 for the variable and check. 5 < 5 This is true, so 5 does work.
Does 4 work? Substitute 4 for the variable and check. 5 < 4. This is false, so 4 does not work.
Does 6 work? Substitute 6 for the variable and check. 5 < 6. This is true, so 6 does work !
Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! 6 is a value that works & is located on the right of 5 on the number line. Shade
on the right. 5
NOTICE!!!
x > 5 has the same graph as 5 < x!
Although the signs point in different directions, for these inequalities, the solutions that make it true are on the
right of 5 on the number line.
AGAIN…. WARNING!
Do NOT shade the direction of the sign!
Instead, only shade the side where the solutions are true.
> does not always mean shade on the right!< does not always means shade on the left!
When do I shade the circle?
OPEN CIRCLE CLOSED CIRCLE
< <> >
=
Practice: Does the solution work?
1. x + 1 = 5 for x = 4 _________________
2. 13 - w = 10 for w = 2 ________________
3. 2 • v = 12 for v = 10 _________________
4. 14 ÷ p = 2 for p = 7 _________________
4 + 1 = 5 yes
14 ÷ 7 = 2 yes
2 ∙ 10 ≠ 12 no
13 - 2 ≠ 10 no
Graph each inequality
1. w 0 0
2. b 4 -4
3. j > 5 5
4. 6 > q 6