1. MTH 10905 Algebra SOLVING LINEAR EQUATIONS WITH A VARIABLE ON ONLY ONE SIDE OF THE EQUATIONS CHAPTER 2 SECTION 4

2. Solving Linear Equations Solving Linear Equations in the form ax + b = c with a variable on only one side of the equal sign. The general procedure is to “Isolate the variable” Steps 1. If the equation contains a fraction then multiply both sides by the LCD to eliminate the fraction. 2. Use the distributive property to remove any parentheses. 3. Combine any like terms that are on the same side of the equal sign. 4. Use the addition property giving you an equation in the form of ax = b 5. Use the multiplication property giving you x = or 1x = 6. Check your answer

3. Linear Equations - Solve Exp: No fractions No parentheses Use the addition property Use the multiplication property Check: 3x – 7 11 (3)(6) – 7 11 18 – 7 11 11 = 11

4. Linear Equations - Solve Exp #30: No fractions - No parentheses Use the addition property Use the multiplication property Check: 25 + 4x = 19 25 + 4(-3/2) 19 25 + -12/2 19 25 - 6 19 19 = 19

5. Linear Equations - Solve Exp: No fractions No parentheses Use the addition property Use the multiplication property Check:-3x – 4 -2 -(3)(-2/3) – 4 -2 6/3 – 4 -2 2 – 4 -2 -2 = -2

6. Linear Equations - Solve Exp #20: No fractions - No parentheses Use the addition property Use the multiplication property Check:6 – 3x = 18 6 – 3(-4) 18 6 + 12 18 18 = 18

7. Linear Equations - Solve Exp: No fractions No parentheses Combine like terms Use the addition property Use the multiplication property Check:15 = 3x + 9 – x 15 (3)(3) + 9 - 3 15 9 + 9 – 3 15 18 – 3 15 = 15

8. Linear Equations - Solve Use the addition property first. If we use the multiplication property first we may or may not get the correct answer and we will usually have to do more work when working with fractions. Exp: 4x – 7 (x + 3) = 2CHECK 4x + (-7)(x) + (-7)(3) = 2 4( ) – 7( ) + (-7)(3) = 2 4x -7x – 21 = 2 -3x – 21 = 2 + - 21 = 2 -3x = 2 + 21 -3x = 23 - 21 = 2 x = 23 - 21 = 2 2 = 2

9. Linear Equations - Solve Exp: CHECK 5x – (4x + 3) = 8 5x + (-1)(4x) + (-1)(3) = 8 5x – (4x + 3) = 8 5x – 4x – 3 = 8 5(11) – ((4)(11) + 3) = 8 x – 3 = 8 55 – (44 + 3) = 8 x = 8 + 3 55 – 47 = 8 x = 11 8 = 8

10. Solving Linear Equations Solving Linear Equations containing decimal numbers. EXP: CHECK:

11. Solving Linear Equations Solving Linear Equations containing decimal numbers. EXP # 39:CHECK: 2.3x – 9.34 = 6.3 2.3x – 9.34 = 6.32.3(6.8) – 9.34 6.3 2.3x = 6.3 + 9.3415.64 – 9.34 6.3 2.3x = 15.65 6.3 = 6.3 x = 15.65/2.3 x ≈ 6.8

12. Solving Linear Equations Solving Linear Equations containing fractions. When working with fractions you must find the LCD and multiply both sides of the equal side by the LCD.

13. Solving Linear Equations EXP:

14. Solving Linear Equations EXP:

15. Solving Linear Equations EXP:

16. Overview Evaluate – find numerical value Simplify – perform operation and combine like terms Solve – find the values of the variables Check – Substitute the value back into the original equation

17. HOMEWORK 2.4 Page 127 - 128 #15, 25, 27, 31, 37, 59, 79, 81