

Simplify the following algebraic expressions.
  6x + 5 + 12x 6
 2(x  9) + 6(x + 2) + 4x

3x^{2} + 12 + 9x  20 + 6x^{2}  x
 (x + 2)(x + 4) + (x + 5)(x  1)
 1.2(x  9)  2.3(x + 4)

(x^{2}y)(xy^{2})

(x^{2}y^{2})(xy^{2})

Simplify the expressions.

(a b^{2})(a^{3} b) / (a^{2} b^{3})

(21 x^{5}) / (3 x^{4})

(6 x^{4})(4 y^{2}) / [ (3 x^{2})(16 y) ]
 (4x  12) / 4
 (5x  10) / (x + 2)

(x^{2}  4x  12) / (x^{2} – 2x – 24)

Solve for x the following linear equations.
 2x = 6
 6x  8 = 4x + 4
 4(x  2) = 2(x + 3) + 7
 0.1 x  1.6 = 0.2 x + 2.3
  x / 5 = 2
 (x  4) / ( 6) = 3
 (3x + 1) / (x  2) = 3
 x / 5 + (x  1) / 3 = 1/5

Find any real solutions for the following quadratic equations.

2 x^{2}  8 = 0

x^{2} = 5

2x^{2} + 5x  7 = 0
 (x  2)(x + 3) = 0
 (x + 7)(x  1) = 9
 x(x  6) = 9

Find any real solutions for the following equations.

x^{3}  1728 = 0

x^{3} =  64
 sqrt(x) = 1
 sqrt(x) = 5
 sqrt(x/100) = 4
 sqrt(200/x) = 2

Evaluate for the given values of a and b.

a^{2} + b^{2} , for a = 2 and b = 2
 2a  3b , for a = 3 and b = 5

3a^{3}  4b^{4} , for a = 1 and b = 2

Solve the following inequalities.
 x + 3 < 0
 x + 1 > x + 5
 2(x  2) < (x + 7)

For what value of the constant k does the quadratic equation x^{2} +2x =  2k have two distinct real solutions?

For what value of the constant b does the linear equation 2x + by = 2 have a slope equal to 2?

What is the y intercept of the line 4x + 6y = 12?

What is the x intercept of the line 3x + y = 3?

What is point of intersection of the lines x  y = 3 and 5x  2y = 22?

For what value of the constant k does the line 4x + ky = 2 pass through the point (2,3)?

What is the slope of the line with equation y  4 = 10?

What is the slope of the line with equation 2x = 8?

Find the x and y intercepts of the line with equation x =  3?

Find the x and y intercepts of the line with equation 3y  6 = 3?

What is the slope of a line parallel to the x axis?

What is the slope of a line perpendicular to the x axis?
Answers to the Above Questions

 6x  1
  6

9x^{ 2} + 8 x  8
 3
 1.1x  20

x^{3}y^{3}

 x^{3}y^{4}


a^{2}
 7x

(1/2)x^{2}y
 x  3
 5
 (x + 2)/(x + 4)

 x = 3
 x = 6
 x = 21/2
 x = 39
 x = 10
 x = 14
 no solution
 x = 1

 solution set {2,2}
 no real solutions
 solution set {1,7/2}
 solution set {2,3}
 solution set {2,8}
 solution set {3}

 x = 12
 x = 4
 no solutions
 x = 25
 x = 1600
 x = 50

Evaluate for the given values of a and b.
 8
 21
 67

 x < 3
 x > 2
 x < 1

k < 1/2

b = 1

(0 , 2)

(1 , 0)

(4 , 1)

k = 10/3

slope = 0

The slope is undefined

x  intercept: (3,0) , no y  intercept.

no x  intercept , y  intercept: (0 , 3)

slope = 0

The slope is undefined.
