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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

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MAT 138 Intermediate Algebra

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  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.

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