1 / 20

MAT 138 Intermediate Algebra

MAT 138 Intermediate Algebra. Lecture 2 Linear Equations. Today's Agenda. Turn in H omework #1 Q & A (30 min.) Quiz #1 (1 hr.) Break (10 min.) Lecture #2 (1.5 hr.). Chapter 2. Linear Equations & Formulas 2.1 Linear Equations in One Variable 2.2 Formulas

bernie
Download Presentation

MAT 138 Intermediate Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MAT 138Intermediate Algebra Lecture 2 Linear Equations

  2. Today's Agenda • Turn in Homework #1 • Q & A (30 min.) • Quiz #1 (1 hr.) • Break (10 min.) • Lecture #2 (1.5 hr.)

  3. Chapter 2 • Linear Equations & Formulas • 2.1 Linear Equations in One Variable • 2.2 Formulas • 2.3 Applications of Linear Equations

  4. Equations • Any sequence of numbers, variables, operation symbols, and/or grouping symbols formed in accordance with the rules of algebra is called an algebraic expression. • A statement that two expressions are equal is an algebraic equation.

  5. Example 1 • Let w = 4and z = –2. • Is the equation (w2 + 2z3 = 0) is true? w2 + 2z3 = 0 (4)2 + 2(–2)3 = 0 16 + 2(–8) = 0 16 – 16 = 0 0 = 0

  6. Example 2 • Let w = 4 and z= –2. • Is the equation (2z3 = w2) is true? 2z3= w2 2(–2)3 = (4)2 2(–8) = 16 –16 = 16

  7. Example 3 • Consider the equation (2x + 5 = 11). • Is x=3 a solution to the equation? 2x+ 5 = 11 2(3) + 5 = 11 6 + 5= 11 11= 11

  8. Property of Equality • The same number may be added, subtracted, multiplied, or divided on both sides of an equation without changing the solution set.

  9. Solving Equations • Clear fractions. • Simplify each side separately. • Isolate the variable terms on one side. • Isolate the variable with a coefficient of 1. • Check your solution(s).

  10. Example 1 Solve the equation (2x+ 5 = 11). 2x+ 5 = 11 2x+ 5 – 5 = 11 – 5 2x = 6

  11. Example 2 Solve the equation (4x– 2x–5 = 3x + 7). 4x– 2x – 5 = 3x+ 7 2x– 5 = 3x+ 7 2x– 5 – 2x= 3x+ 7 – 2x –5 = x+ 7 –5 – 7 = x + 7 – 7 –12 = x

  12. Example 3 Solve the given equation. 2(k-5) = -2k + 6 2k - 10 = -2k + 6 2k - 10 + 2k = -2k + 2k + 6 4k - 10 = 6 4k - 10 + 10 = 6 + 10 4k = 16 k = 4

  13. Example 4 Solve the given equation.

  14. Example 5 Solve the given equation.

  15. Formulas • A formula is an equation in which variables are used to describe a relationship. • We use formulas to compute areas and perimeters of shapes, to convert between different units, to calculate interest, to compute distances, etc.

  16. Example 1 • Here's a formula for calculating distance: • d = rt where d represents distance, r represents rate, and t represents time. • If a truck traveled at 60 mph for 2 hours, how far would it travel? • How long would it take a truck to travel 100 miles at 50 mph? • On average, how fast would a truck have to travel to cover 200 miles in 4 hours?

  17. Example 2 • Here's a formula for calculating the area of a triangle: • A = 0.5(bh) where A represents area, b represents the base, and h represents the height. • Calculate the area of the following triangle: 4 8

  18. Example 3 • A = 0.5(bh) where A represents area, b represents the base, and h represents the height. • If the area of the triangle is 12, calculate the height of the following triangle: A=12 h 6

  19. Real-world Problems • Break the problem down into phrases. • Translate each phrase to English using variables to represent the unknown values. • Put the phrases together into an equation. • Solve the equation. • Check the answer using the words in the original problem.

  20. Summary • We learned about algebraic equations. • We learned how to solve equations. • We learned how to use formulas. • We learned how to apply formulas and equations to real-world problems.

More Related