MTH095
Intermediate Algebra
Math for Calculus

vs.

MTH092
Quantitative Literacy
Math for "Real" Life

Which class is right for you?
Is calculus in your future or NOT?

Calculus Path

Statistics Path

Rational Equations

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!!!

Balancing Blood Alcohol

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

Radical Equations

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

Compunding Interest Makes Cents

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`

Disclaimer:

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.

What's next?

MTH111
College Algebra
Pre-Calculus, part 1

vs.

MTH105
Math in Society
Math for "Real" Life