Solving Linear Inequalities Remember…. “I’m bigger than you are….” > OR “The alligator...
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Transcript of Solving Linear Inequalities Remember…. “I’m bigger than you are….” > OR “The alligator...
Solving Linear Inequalities
Remember….
“I’m bigger than you are….” >OR“The alligator eats the bigger number….”
<
Solving an inequality with a variable on one side
5y – 8 < 12
You do: 11y – 9 > 13
Solving an inequality with a variable on one side
2x + 1 < 6x - 1
Solving an inequality with a variable on both sides
You do: 7x + 9 > 10 x -12
Solving an inequality with a variable on both sides
-2 < x < 1
A COMPOUND INEQUALITY is two simple inequalities joined by “and” or “or”.
x < -1 or x > 2
All real numbers that are greater than or equal to -2 AND less than 1.
All real numbers that are less than -1 OR greater than or equal to 2
Solving an “AND” compound inequality
-2 < 3t – 8 < 10
Solving an “AND” compound inequality
You do: -9 < y + 4 < 10
Solving an “OR” compound inequality
2x + 3 < 5 or 4x – 7 >9
Solving an “OR” compound inequality
You do: 6x + 9 < 3 or 3x – 8 > 13
Solving Linear Inequalities
Remember….
“I’m bigger than you are….” >OR“The alligator eats the bigger number….”
<
Solving an Absolute Value Equation
The absolute value of a number |x| is the distance the number is from 0 on a number line.
|x| = 5
|2x - 5| = 9
Solving an Absolute Value Equation
You do: |6x - 3| = 15
Solving an Absolute Value Equation
2|3x - 3|+ 5 = 13
Solving an Absolute Value Equation
You do: -|3x + 8|-6 = 15
Solving an Absolute Value Inequality of the form: |ax + b| < c
|2x + 7| < 11
Less thand
-c < |ax + b| < c
Solving an Absolute Value Inequality of the form: |ax + b| < c
You do: |4x - 9| < 21
-c < |ax + b| < c
Solving an Absolute Value Inequality of the form: |ax + b| < c
You do: 2|x - 5| - 8 < 20
-c < |ax + b| < c
Solving an Absolute Value Inequality of the form: |ax + b| > c
|3x - 2| > 8
ax + b < -c or ax + b > c
Greator than
Solving an Absolute Value Inequality of the form: |ax + b| > c
You do: |-x + 1| > 15
ax + b < -c or ax + b > c
Solving an Absolute Value Inequality of the form: |ax + b| > c
You do: 3|-2x| > 15
ax + b < -c or ax + b > c