Math095- Chapter 3- Linear Equation-Revised (1).pptx

Math095- Chapter 3- Linear Equation-Revised (1).pptx

1. Chapter 3 Linear Equations Section 3-1 Addition Property of Equality 1. Solve linear equations, using the addition property of equality 2. Translate mathematics expressions into English and English expressions into mathematics.

2. Solve linear equations, using the addition property of equality solving the equation is The process of find the solution(s) of an equation variable = constant 1) m - 7 = - 8 3 ) x + 7 - 3 = 6 -11 An equation states that two mathematical expressions are equal . 2) t + 6 = 5

3. 4 ) – 7 – 8 = – 8 x – 15 + 9 x Solving equations. Simplify your answer 5 ) 6 (a + 3) – 5 a = 8 6 ) 13y – 4 (3y + 5) = 12

4. 7 ) – 10( 2 x + 4) + 7( 3 x – 2) – 7 = 5 – 9

5. Translating English sentences into mathematics sentences. Search for operation key words. Translate ( is / were ) into equal sign ( = ) Use a variable for some number 2. Thirty – five is some number subtracted from eight. 1. Some number minus two is equal to nine . 4. Six more than m is twelve . 3. The difference between a number and negative four is Thirteen.

6. Translating English sentences into mathematics sentences. 1. Five more than some number is negative 12 . 5 – x = -12 x – 5 = - 12 x + 5 = - 12 -12 + x = 5 2. Eight less than some number is negative twenty-five . 8 – x = -25 x – 8 = - 25 x – 25 = - 8 D. x +8 = - 25 3. Twenty-nine is some number decreased by eleven . 28 = 11 – x x – 11 = 28 28 = x – 11 D. 28 = x + 11 4. - 9 subtracted from some number is 25 . x + 9 = 25 ; 16 x – 9 = 25 ; 34 – 9 + x = 25 ; 34 D. x + 9 = 25 ; 2 4

7. Section 3-2 Multiplication Property of Equality Solve equations by using the multiplication property of equality.

8. 1 . 9 y = -27 Solve equations       Translate from English to a mathematical sentence and solve. Use x as the variable. -6 times a number is 18

9. 1 ) 24 x + 7 – 26 x = 8 – 9 2 ) –5 (3a – 1) – 12 a = 2 3 ) 25c + 8 – 28c = 4 – 5

10. 1. Translating English sentences into mathematics sentences and solve. use x as the variable . The product of four and some number is negative twenty- six. x – 4 = – 26 4 x = – 26 x + 4 = – 26 – 26 x = 4 T he solution is x = Solve  

11. Section 3-3 Solve equation using Addition & Multiplication Property of Equality B. Solve linear equations, using both the addition and multiplication property of equality. B. Determine whether an equation is an Identity or contradiction .

12. 1 ) 6 – 2 x = 6 x – 10 x + 14 2 ) 10 (2 + 4n) – 22n = 6(n – 1) Solve equations 1 .Simplify each side of equation 2. Move like terms

13. 3 ) 5(4a – 1) – 4 = 15a + 6 Solve equations

14. Determine whether the equation is an identity or a contradiction . An Identity is An equation that is true for all values of the variable for which the equation is defined . I dentity Solution is “ all real numbers ” 3( w +2) - 4 = w + 2 w + 2 Same result on both sides of equation The variable can be Any real number

15. Determine whether the equation is an identity or a contradiction . A contradiction is An equation that has no solution. NO SOLUTION 6 ( w +1) -2 = 6w + 8 The result on both sides are Not equal No Solution

16. Determine whether the equation is an identity or a contradiction and indicate solutions 1) 6 x – 3 ( x + 3) = 6 x – 6 – 3( x – 4) 2) 4a + 9 = 4(a +1) +5

17. Determine whether the equation is an identity or a contradiction and indicate solutions 3) 8w – 4 (w + 4) = 4(2w – 4) – 4(w – 5) 4) 4 (c + 2) = 8c + 4 – 4c + 4