ALGEBRA 1 NOTES
NAME:____________________________
SOLVING INEQUALITIES
☺ WHAT IS AN INEQUALITY? _______________________________________________
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DRAW IN THE SYMBOL FOR EACH TYPE OF INEQUALITY
SIGN
GREATER THAN
LESS THAN
GREATER THAN OR EQUAL TO
LESS THAN OR EQUAL TO
" WHEN GRAPHING AN INEQUALITY, WHEN WILL YOU USE A CLOSED DOT? ______________________
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" WHEN GRAPHING AN INEQUALITY, WHEN WILL YOU USE AN OPEN CIRCLE? ______________________
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COMPLETE THE TABLE WITH THE CORRECT TYPE (CLOSED OR OPEN) OF CIRCLE FOR EACH TYPE OF
INEQUALITY
CIRCLE
GREATER THAN
LESS THAN
GREATER THAN OR EQUAL TO
LESS THAN OR EQUAL TO
LOOK AT THE FOLLOWING INEQUALITIES AND THEIR GRAPHS.
€
A.
!!c < −2
B.
!!4 ≤ m
€ " WHAT DOES THE OPEN CIRCLE MEAN IN EXAMPLE A? IS -2 A SOLUTION TO THE INEQUALITY?
" BOTH INEQUALITIES HAVE A LESS THAN SYMBOL, WHY THEN DO THE GRAPHS GO IN OPPOSITE
DIRECTIONS?
Algebra I
☺
Name: __________________
GRAPHING INEQUALITIES – READ!!!!
THERE ARE SEVERAL THINGS YOU NEED TO KEEP IN MIND WHEN GRAPHING AN INEQUALITY.
1. YOUR NUMBER LINE MUST HAVE ARROWS ON THE END.
2. YOU MUST HAVE AT LEAST 3 NUMBERS ON THE NUMBER LINE. YOU WILL INCLUDE THE
ANSWER, ONE NUMBER SMALLER THAN THE ANSWER, AND ONE NUMBER HIGHER THAN THE
ANSWER. (SEE EXAMPLES A AND B ON PREVIIOUS PAGE.)
3. YOU MUST INCLUDE THE PROPER CIRCLE (CLOSED OR OPEN).
4. DRAW YOUR ARROW DARK ENOUGH TO DISTINGUISH IT FROM THE NUMBER LINE.
5. YOU MUST INCLUDE AN ARROW AT THE END OF YOUR SHADING.
" GRAPH THE FOLLOWING INEQUALITIES. (FOLLOW THE DIRECTIONS FROM ABOVE!)
€
A.
!!x > 6
B.
!!6 < x
€
C.
!!x ≥ 6
D.
!!6 ≤ x
" IF YOU ARE HAVING TROUBLE DECIDING WHICH DIRECTION TO SHADE, FOLLOW THESE STEPS…
o SUBSTITUTE A NUMBER IN FOR X. YOU CAN PICK ANY NUMBER AS LONG AS IT IS NOT THE
€
€
SOLUTION.
o IF THE RESULTING INEQUALITY IS TRUE, SHADE TOWARD THAT NUMBER ON THE NUMBER
LINE.
o IF THE RESULTING INEQUALITY IS FALSE, SHADE AWAY FROM THAT NUMBER ON THE
NUMBER LINE.
☺
YOU SOLVE INEQUALITIES THE SAME WAY YOU SOLVE EQUATIONS!!!
EXAMPLES: SOLVE EACH INEQUALITY AND GRAPH THE SOLUTION ON AN NUMBER LINE. YOU WILL NEED TO
DRAW YOUR OWN NUMBER LINE.
x
+ 7 < 10
4
2. 4 + 6x ≥ 28
3. 2c − 6 ≤ 3c − 2
4. t + 2.5 ≤ 4.8
1.