solving inequalities pages 142 - 144. solving inequalities ● solving inequalities follows the same...
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Solving Inequalities
Pages 142 - 144
Solving Inequalities●Solving inequalities follows the same procedures as solving equations.
●There are a few special things to
consider with inequalities:●We need to look carefully at the inequality sign.●We also need to graph the solution set.
Review of Inequality Signs
> greater than
< less than< less than
≥ greater than or equal
≤ less than or equal
How to graph the solutions> Graph any number greater than. . .
open circle, line to the right
< Graph any number less than. . . open circle, line to the left
≥ Graph any number greater than or equal to. . .
closed circle, line to the right
≤ Graph any number less than or equal to. . . closed circle, line to the left
Solve the inequality:
x + 4 < 7 -4 -4
x 3
●Subtract 4 from each side.
●Keep the same inequality sign.
●Graph the solution.
●Open circle, line to the left.
30
<
There is one special case.
●Sometimes you may have to reverse the direction of the inequality sign!!
●That only happens when you
multiply or divide both sides of the inequality by a negative number.
Solving an Inequality
Solve 5 + y <13
5 + y < 13
Subtract 5 to each side.
Write original inequality.
Simplify.
5 + y - 5 < 13 - 5
y < 8
To graph y < 8, use an open dot and draw the arrow pointing to the left.
73 4 5 6 982 10
Then graph the solution.
Example 1:
Solving an Inequality
Solve a – 3 > -5
a – 3 > -5
Add 3 to each side..
Write original inequality.
Simplify.
a – 3 + 3 > -5 + 3
a > -2
To graph a > -2 use a closed dot and draw the arrow pointing to the right.
Then graph the solution.
2–2 –1 0 1 43–3 5
Example 2:
Solve: -3y + 5 >23
-5 -5
-3y > 18
-3 -3
y < -6
●Subtract 5 from each side.
●Divide each side by negative 3.
●Reverse the inequality sign.
●Graph the solution.
• Open circle, line to the left.
0-6
Example 3:
Solving Inequalities
Solving Inequalities
Try these:
●Solve 2x+3>x+5
●Solve - c - 11>23
●Solve 3(r-2)<2r+4