The rules for solving inequalities are the same as solving equations, WITH ONE EXCEPTION : IF YOU DIVIDE BY A NEGATIVE, THE INEQUALITY FLIPS Ex: -4x > 12 -4 -4 F L I P x < -3
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The rules for solving inequalities
are the same as solving equations,
WITH ONE EXCEPTION:
IF YOU DIVIDE BY A NEGATIVE,
THE INEQUALITY FLIPS
Ex:
-4x > 12-4 -4F
L
I
P
x < -3
2x + 6 < -10
Inequalities similar to unit 1 equations
2x + 6 < -10-6 -6
2x < -10
Inequalities similar to unit 1 equations
Subtract 6
2x + 6 < -10-6 -6
2x < -102 2
Inequalities similar to unit 1 equations
Divide by 2
2x + 6 < -10-6 -6
2x < -102 2
x < -5
Inequalities similar to unit 1 equations
NOTE: The inequality DOES NOT FLIP
because we divided by a positive 2
3(x – 4) < 2
Inequalities including the distributive property
3(x – 4) < 2
3x – 12 < 2
Inequalities including the distributive property
distribute
3(x – 4) < 2
3x – 12 < 2
+12 +123x < 14
Inequalities including the distributive property
Add 12
3(x – 4) < 2
3x – 12 < 2
+12 +123x < 143 3
Inequalities including the distributive property
Divide by 3
3(x – 4) < 2
3x – 12 < 2
+12 +123x < 143 3
x < 143
Inequalities including the distributive property
NOTE: The inequality DOES NOT FLIP
because we divided by a positive 3
x + 5 < 61
2
Inequalities including fractions
x + 5 < 61
2-5 -5
x < 11
2
Inequalities including fractions
Subtract 5
x + 5 < 61
2-5 -5
x < 11
22 2
Inequalities including fractions
Multiply by 2
1x < 2
x + 5 < 61
2-5 -5
x < 11
22 2
1x < 21 1
Inequalities including fractions
Divide by 1
x + 5 < 61
2-5 -5
x < 11
22 2
1x < 21 1x < 2
Inequalities including fractions
NOTE: The inequality DOES NOT FLIP
because we divided by a positive 1
3x – 8 < 5x + 2
Inequalities with variables on both sides
3x – 8 < 5x + 2-5x -5x-2x – 8 < 2
Inequalities with variables on both sides
Subtract 5x
3x – 8 < 5x + 2
+8+8
-5x -5x-2x – 8 < 2
-2x < 10
Inequalities with variables on both sides
Add 8
3x – 8 < 5x + 2
+8+8
-5x -5x-2x – 8 < 2
-2x < 10-2 -2
Inequalities with variables on both sides
Divide by NEGATIVE 2
3x – 8 < 5x + 2
+8+8
-5x -5x-2x – 8 < 2
-2x < 10-2 -2
x > -5
Inequalities with variables on both sides
3x – 8 < 5x + 2
+8+8
-5x -5x-2x – 8 < 2
-2x < 10-2 -2
x > -5
Inequalities with variables on both sides
NOTE: The inequality FLIPS
because we divided by a NEGATIVE 2
-2(2x – 3) > -8(x + 1)
Inequalities with distributive property AND variables on both sides
-2(2x – 3) > -8(x + 1)
-4x + 6 > -8x – 8
Inequalities with distributive property AND variables on both sides
Distribute first!
-2(2x – 3) > -8(x + 1)
-4x + 6 > -8x – 8 +8x +8x
4x + 6 >-8
Inequalities with distributive property AND variables on both sides
Add 8x
-2(2x – 3) > -8(x + 1)
-4x + 6 > -8x – 8 +8x +8x
4x + 6 >-8-6 -6
4x > -14
Inequalities with distributive property AND variables on both sides
Subtract 6
-2(2x – 3) > -8(x + 1)
-4x + 6 > -8x – 8 +8x +8x
4x + 6 >-8-6 -6
4x > -144 4
x > -7
2
Inequalities with distributive property AND variables on both sides
Divide by 4
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