1 / 23

2.1 – Linear Equations in One Variable

2.1 – Linear Equations in One Variable. Objective – Solve linear equations using properties of equality. Solve linear equations that can be simplified by combining like terms. -Solve linear equations involving fractions. Why is this important?. Linear Equations.

rich
Télécharger la présentation

2.1 – Linear Equations in One Variable

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. 2.1 – Linear Equations in One Variable Objective – Solve linear equations using properties of equality. Solve linear equations that can be simplified by combining like terms. -Solve linear equations involving fractions

  2. Why is this important?

  3. Linear Equations • Linear Equations in one variable – • A linear equation in one variable is an equation that can be written in the form ax + b = c Where a, b, and c are real numbers and a 0 • The Addition and Multiplication Properties of Equality • If a, b, and c, are real numbers, then • a=b and a+c = b – c are equivalent equations • Also a =b and ac = bc are equivalent equations as long as c 0

  4. Solve: Addition property of equality 2 x + 5 = 9 2x + 5 -5 = 9 -5 2x = 4 2x = 4 2 2 x = 2 Subtract 5 from both sides Simplify Divide both sides by 2 Simplify

  5. Check • To see that 2 is the solution, replace x in the original equation with 2. 2 x + 5 = 9 2 (2) + 5 = 9 4 + 5 = 9 9 = 9

  6. Give it a try 3 x + 6 = 12 3x + 6 – 6 = 12 –6 3x = 6 3x = 6 3 3 x = 2

  7. Check 0.6 = 2 – 3.5c 0.6 = 2 – 3.5 (0.4) 0.6 = 2 – 1.4 0.6 = 0.6

  8. Give it a try! 4.5 = 3 + 2.5 x 4.5 – 3 = 3 + 2.5 x – 3 1.5 = 2.5 x 1.5 = 2.5 x 2.5 2.5 0.6 = x

  9. Solve – Combining like terms -6 x – 1 + 5x = 3 -6x – 1 + 5x = 3 -x – 1 = 3 -x – 1 + 1 = 3 + 1 -x = 4 -1 -1 x = -4

  10. Give it a try! -2x + 2 – 4x = 20 -2x + 2 – 4x = 20 -6x + 2 = 20 -6x + 2 – 2 = 20 – 2 -6x = 18 -6 -6 x = -3

  11. Solve: Distributive Property 2 (x – 3) = 5 x – 9 2(x – 3) = 5 x – 9 2x – 6 = 5 x – 9 2x – 6 – 5x = 5x –9 – 5x -3 x – 6 = - 9 -3 x – 6 + 6 = - 9 + 6 -3x = -3 -3 -3 x = 1

  12. Give it a try! 4 (x – 2) = 6x –10 4x – 8 = 6x – 10 2 = 2 x 1 = x

  13. Solve: Adding/Subtracting Fractions

  14. Give it a try!

  15. Solve: Multiplying Fractions

  16. Give it a try!

  17. Solve: Decimals 0.3x + 0.1 = 0.27 x – 0.02 100(0.3x +0.1) = 100 (0.27x – 0.02) 100(0.3x) + 100 (0.1) = 100(0.27x) – 100(0.02) 30 x + 10 = 27 x – 2 30 x – 27 x = -2 –10 3 x = -12 3x = -12 3 3 x = - 4

  18. Give it a try! 0.2x +0.1 = 0.12x – 0.06 100 (0.2 x + 0.1) = 100 (0.12 x – 0.06) 20 x + 10 = 12 x – 6 20 x – 12 x = -6 – 10 8 x = -16 x = -2

  19. Solve: Contradiction 3x + 5 = 3(x+2) 3 x + 5 = 3 (x + 2) 3 x + 5 = 3x + 6 3 x + 5 – 3 x = 3 x + 6 – 3 x 5 = 6 This is a false statement…The original equation has no solution. Its solution set is written either by { } or O. This equation is a contradiction.

  20. Give it a try! 5 x – 1 = 5(x+3) 5 x – 1 = 5 x + 15 -1 = 15 { }

  21. Solve: Identity 6 x – 4 = 2 + 6 (x –1) 6x – 4 = 2 + 6x – 6 6 x – 4 = 6 x – 4 {x/ x is a real number} 6 x – 4 + 4 – 6x – 4 + 4 6 x = 6 x 6x – 6x = 6 x – 6x 0 = 0 This equation is called an identity!

  22. Give it a try! -4(x – 1) = -4x –9 +13 -4x + 4 = -4x + 4 {x / x is a real number}

  23. Put it in words! Solving a linear equation in one variable • Step 1: Clear the equation of fractions by multiplying both sides of the equation by the LCD • Step 2: Use distributive property to remove grouping symbols such as parentheses. • Step 3: Combine like terms. • Step 4: Isolate the variable by adding, subtracting, multiplying, dividing (equality properties) • Step 5: Check the solution in the original equation.

More Related