Warm Up

1
Warm Up Solve each equation.
1. 2x 7x 15 2.
x 3

3y 21 4 2y
y 5
z 1
3. 2(3z 1) 2(z 3)
4. 3(p 1) 3p 2
no solution
b lt 3
5. Solve and graph 5(2 b) gt 52.
2
Example 1A
Solve the inequality and graph the solutions.
y 4y 18
To collect the variable terms on one side,
subtract y from both sides.
Since 18 is added to 3y, subtract 18 from both
sides to undo the addition.
Since y is multiplied by 3, divide both sides by
3 to undo the multiplication.
6 y (or y ? 6)
3
Example 1B
Solve the inequality and graph the solutions.
4m 3 lt 2m 6
To collect the variable terms on one side,
subtract 2m from both sides.
Since 3 is subtracted from 2m, add 3 to both
sides to undo the subtraction
Since m is multiplied by 2, divide both sides by
2 to undo the multiplication.
4
Example 2A
Solve the inequality and graph the solutions.
5(2 r) 3(r 2)
Distribute 5 on the left side of the inequality
and distribute 3 on the right side of the
inequality.
5(2 r) 3(r 2)
5(2) 5(r) 3(r) 3(2)
Since 6 is subtracted from 3r, add 6 to both
sides to undo the subtraction.
10 5r 3r 6
16 - 5r 3r
Since 5r is subtracted from 16 add 5r to both
sides to undo the subtraction.
16 8r
5
Example 3A
Solve the inequality.
2x 7 5 2x
2x 7 5 2x
Subtract 2x from both sides.
?
7 5
True statement.
The inequality 2x - 7 5 2x is an identity.
All values of x make the inequality true.
Therefore, all real numbers are solutions.
6
Example 4A
Solve the inequality.
4(y 1) 4y 2
4(y 1) 4y 2
Distribute 4 on the left side.
4(y) 4(1) 4y 2
4y 4 4y 2
Subtract 4y from both sides.
?
4 2
False statement.
No values of y make the inequality true. There
are no solutions.