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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 = 8x 15 + 9x Solving equations. Simplify your answer 5) 6 (a + 3) 5a = 8 6) 13y 4 (3y + 5) = 12
- 4. 7) 10( 2x + 4) + 7( 3x 2) 7= 5 9
- 5. Translating English sentences into mathematics sentences. 1. Search for operation key words. 2. Translate (is / were) into equal sign (=) 3. 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. A. 5 x = -12 B. x 5 = - 12 C. x + 5 = - 12 D. -12 + x = 5 2. Eight less than some number is negative twenty-five. A. 8 x = -25 B. x 8 = - 25 C. x 25 = - 8 D. x +8 = - 25 3. Twenty-nine is some number decreased by eleven. A. 28 = 11 x B. x 11 = 28 C. 28 = x 11 D. 28 = x + 11 4. - 9 subtracted from some number is 25 . A. x + 9 = 25 ; 16 B. x 9 = 25 ; 34 C. 9 + x = 25 ; 34 D. x + 9 = 25 ; 2 4
- 8. Section 3-2 Multiplication Property of Equality Solve equations by using the multiplication property of equality.
- 9. 1. 9 y = -27 Solve equations 2. 7 = 9 3. 3 17 = 15 4. 5 8 = 20 Translate from English to a mathematical sentence and solve. Use x as the variable. -6 times a number is 18
- 10. 1) 24x + 7 26x = 8 9 2) 5 (3a 1) 12 a = 2 3) 25c + 8 28c = 4 5
- 11. 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. A. x 4 = 26 B. 4 x = 26 C. x + 4 = 26 D. 26 x = 4 The solution is x = 2. Solve 5 8 = 20
- 12. 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.
- 13. 1) 6 2x = 6x 10x + 14 2) 10 (2 + 4n) 22n = 6(n 1) Solve equations 1.Simplify each side of equation 2. Move like terms
- 14. 3) 5(4a 1) 4 = 15a + 6 Solve equations
- 15. 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. Identity Solution is all real numbers 3(w +2) - 4 = w + 2w + 2 Same result on both sides of equation The variable can be Any real number
- 16. 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
- 17. Determine whether the equation is an identity or a contradiction and indicate solutions 1) 6x 3 (x + 3) = 6 x 6 3( x 4) 2) 4a + 9 = 4(a +1) +5
- 18. 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