In problems 1-8, solve the given equation.
 
 

1.

2x³+10x²+12x = 0.

2.

5x²-2x-8 = 3x²+x+1

3.

[(6x²-7x-3)/( 2x-3)] = 1

4.

x⁴-8x²+15 = 0

5.

x³-2x²-5x = -10 [Hint: use grouping]

6.

[Ö(2x+7)]-x = 2

7.

⁴/_x - ⁵/₃ = ^x/₆

8.

|3x+2| = 7

9.

Write an inequality to represent each interval:

 
 

a.

[ -2, 3 ]

 
 
 
 

b.

( 4, ¥ )

 
 
 
 

c.

[ -1, 5 )

 
 
 
 

d.

( -¥, 1 ]

 
 
 
 

e.

( 2, 7 )

 
 
 
 

10.

Use a real number line to graph the values of x for which each inequality is satisfied.

 
 

a.

x < 2

 
 
 
 

b.

x ³ 5

 
 
 
 

c.

-3 < x £ 6

 
 
 
 

d.

1 < x < 2

 
 
 
 

e.

3 £ x £ 5

 
 
 
 

In problems 11-15, solve the given inequality and sketch the solution on the real number line.
 
 

11.

2x > 3

12.

x+7 £ 12

13.

-4 < [(2x-3)/ 3] < 4

14.

|x| < 3

15.

|x-3| ³ 10

16.

Find the slope of the line passing through the points ( -1, 1 ) and ( 2, 7 ).

17.

Find the slope-intercept form of the equation for the line passing through the points ( -1, 1 ) and ( 2, 7 ).

18.

Find an equation for the line through the point ( 2, 3 ) with slope m = -2.

19.

Draw a graph of the line y = 2x-1.

20.

Determine the slope of each line depicted below.