Download HAPPY MONDAY!!! Solving Inequalities Using Addition or

November 23, 2015
HAPPY MONDAY!!!
Solving Inequalities Using Addition or Subtraction.
Assignment:
p. 288 #12-32 even, 34-40 all
November 23, 2015
Warm-up:
Fill in the blanks with the appropriate inequality (> or <)
1.
7>5
2. 16 < 21
3.
-9 < -4
4. -13 > -16
5. 13 < 16
November 23, 2015
set builder notation:
{ x | inequality answer }
read "all numbers x such that - (inequality answer)"
EXAMPLE:
m + 19 > 56
m + 19 > 56
m + 19 - 19 > 56 - 19
m > 37
{m| m > 37}
all numbers m such that m is greater than 37
November 23, 2015
Solve each inequality. Then check your solution, and graph
it on a number line.
1. a - 12 < 6
2. 2x < x + 1
a - 12 + 12 < 6 + 12
2x - x < x - x + 1
a < 18
x<1
{ a| a < 18 }
{ x| x < 1 }
3. x + 1/3 > 4
4. 2x + 3 > x + 5
x + 1/3 - 1/3 > 4 - 1/3
2x - x + 3 > x - x + 5
x > 3 2/3
x+3>5
{ x| x > 3 2/3 }
x+3-3>5-3
x>2
{ x| x > 2}
November 23, 2015
Solve each inequality. Then check your solution.
5. x + 1/8 < 1/2
6. 3x - 9 < 2x + 6
x + 1/8 - 1/8 < 4/8 - 1/8
3x - 2x - 9 < 2x - 2x + 6
x < 3/8
x-9<6
{ x| x < 3/8 }
x-9+9<6+9
x < 15 { x| x < 15 }
7. -0.17x - 0.23 < 0.75 - 1.17x
8. 3(r - 2) < 2r + 4
-0.17x+1.17 x-0.23<0.75-1.17x+1.17x 3r - 6 < 2r + 4
x - 0.23 < 0.75
3r - 2r - 6 < 2r - 2r + 4
x - 0.23 + 0.23 < 0.75 + 0.23
r-6<4
x < 0.98
r-6+6<4+6
{ x| x < 0.98 }
r < 10
{ r| r < 10 }
November 23, 2015
Phrases for inequalities
Match the phrase to the symbol (<, <, >, or >)
a) more than >
b) fewer than <
c) at least >
d) no more than <
e) less than <
f) greater than or equal to >
g) at most <
h) greater than >
i) less than or equal to <
j) no less than >
November 23, 2015
Define a variable, write an inequality, and solve each
problem. Then check your solution.
9. A number decreased by -4 is at least 9.
x - (-4) > 9
x+4>9
x+4-4>9-4
{ x| x > 5 }
x>5
10. Three times a number is less than twice the number
added to 8.
3x < 2x + 8
3x - 2x < 2x - 2x + 8
x<8
{ x| x < 8 }