Intermediate Algebra

Math for Calculus

Quantitative Literacy

Math for "Real" Life

Is calculus in your future or NOT?

Solve for `x` in `3/(x+2)-4/(x-5)=2/(x^2-3x-10)`

Factor all denominators:

`3/(x+2)-4/(x-5)=2/((x+2)(x-5))`

Find the lowest common denominator:

`LCD=(x+2)(x-5)`

Multiply all terms in the equation by the LCD:

`(x+2)(x-5)*3/(x+2)-(x+2)(x-5)*4/(x-5)` `=(x+2)(x-5)*2/((x+2)(x-5))`

Divide out the common factors:

`cancel((x+2))(x-5)*3/cancel(x+2)-(x+2)cancel((x-5))*4/cancel(x-5)`
`=cancel((x+2)(x-5))*2/cancel((x+2)(x-5))`

The equation simplifies to:

`3(x-5)-4(x+2)=2`

Simplify:

`3x-15-4x-8=2`

`x=-25`

CHECK:

`3/((-25)+2)-4/((-25)-5)=-3/23+2/15=(-45+46)/(23*15)``=1/345`

`2/((-25)^2-3(-25)-10)=2/(625+75-10)=1/690=1/345`

It checks!!!

Problem Situation: Calculating Blood Alcohol Content

`BAC = -0.015*"hours"+(2.84*"drinks")/("Weight"*"gender")`

Hours | Blood Alcohol Content |
---|---|

0 | 0.116 |

1 | 0.101 |

2 | 0.086 |

3 | 0.071 |

4 | 0.056 |

5 | 0.041 |

Solve for `x` in `sqrt(10-x^2)-x=2`

Isolate the radical:

`sqrt(10-x^2)=x+2`

Square both sides:

`(sqrt(10-x^2))^2=(x+2^2)`

Clean up:

`10-x^2=(x+2)(x+2)`

`10-x^2=x^2+4x+4`

Collect all terms on one side:

`0=2x^2+4x-6`

Pray you can factor, or use Quadratic Formula:

`0=2(x^2+2x-3)`

`0=2(x+3)(x-1)`

So, `x=-3` or `x=1`

CHECK:

`sqrt(10-(-3)^2)-(-3)=sqrt(1)+3=4`, but NOT `2`

`x=-3` does not check!?!

`sqrt(10-(1)^2)-(1)=sqrt(9)-1=3-1=2`, This Checks!!!

So, only `x=1` is a solution

Problem Situation: The Value of a CD

Suppose you invest $1,000 principal in a two-year CD, advertised with an annual percentage rate (APR) of 2.4%, where compounding occurs monthly.

`I=P*r*t`

You should check with your advisor before taking a math class leading to calculus. Algebra classes are known to cause stress, anger, depression, and occassionally rashes, as well as lead to calculus. Please consult a physician if negative symptoms persist.

College Algebra

Pre-Calculus, part 1

Math in Society

Math for "Real" Life