CAPPS forms? 1.1 questions?? 1.2 Linear and Rational Equations

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Presentation transcript:

College Algebra 1.2 & 1.3 Obj: set up and solve linear and rational equations CAPPS forms? 1.1 questions?? 1.2 Linear and Rational Equations 1.3 Models and Applications

1.2 Solving Equations Review Solve 2(x – 3) – 17 = 13 – 3(x + 2) 2x – 6 – 17 = 13 – 3x – 6 2x – 23 = 7 – 3x 5x = 30 x = 6 The calculator can also solve the equation.

Calculator Using the same equation 2(x – 3) – 17 = 13 – 3(x + 2) Go to Y= and input the left side of the equation into Y1 and the right side into Y2. Go to CALC and scroll down to INTERSECT. First curve? ENTER Second curve? ENTER Guess? Put cursor on intersection point and enter.

Practice Solve and check:4(2x + 1) = 29 + 3(2x – 5) Remember that you can solve algebraically, graphically, or numerically. Solve and check: Hint: multiply by the LCD (12) first!

Rational Equations Definition – an equation with a variable in the denominator Example: 1. Set the domain. 2. Multiply by the LCD. 3. Simplify both sides. 4. Isolate the variable.

Practice Problems Solve for x. Given and , find the values of x for which y1 = y2.

Types of Equations Identity – is true for all values of x 4(x – 7) = 4x - 28 Conditional Equation – is true for at least one value of x 8x + 2x = 9x Contradiction – is not true for any value of x 4x – 7 = 4(x – 1) + 3

1.3 Formulas Solve literal equations for a given variable. (table on page 123) Given a formula, use the same process used before to solve linear equations. Example: Solve for x.

Applications Formulas to remember d = r * t I = prt original(1 + %) = part profit = revenue – cost rate of work * time worked = part completed

Examples After 20% reduction, you purchase a television for $336. What was the television’s price before the reduction? An investment adviser invested $14,000 in two accounts. One investment earned 8% annual simple interest, and the other investment earned 6.5% annual simple interest. The amount of interest earned for 1 year was $1024. How much was invested in each account?

Assignment 1.2 Page 118 3, 9, 17, 25, 31, 41, 45, 51, 61, 63, 65 1.3 Page 132 1, 29, 35, 37, 39, 43, 45, 55, 57, 73, 77