MTH 112 Elementary Functions Chapter 6 Trigonometric Identities, Inverse Functions, and Equations
MTH 10905 Algebra SOLVING LINEAR EQUATIONS WITH A VARIABLE ON ONLY ONE SIDE OF THE EQUATIONS CHAPTER...
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Transcript of MTH 10905 Algebra SOLVING LINEAR EQUATIONS WITH A VARIABLE ON ONLY ONE SIDE OF THE EQUATIONS CHAPTER...
MTH 10905Algebra
SOLVING LINEAR EQUATIONS WITH A VARIABLE ON ONLY ONE SIDE OF
THE EQUATIONS
CHAPTER 2 SECTION 4
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”
Steps1. 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 = b5. Use the multiplication property giving you x = or 1x =6. Check your answer
ba
ba
Linear Equations - Solve
Exp: 3 7 11
3 7 7 11 7
3 18
3
x
x
x
3x 18
3
18 3
6
x
x
No fractionsNo parentheses Use the addition property
Use the multiplication property
Check:
3x – 7 11(3)(6) – 7 11 18 – 7 11 11 = 11
???
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
?
??
23
4664
2519419425
x
x
xx
x
Linear Equations - Solve
Exp: -3 4 2
3 4 4 2 4
-3 2
3
x
x
x
3x
23
2 3
x
No fractionsNo 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
????
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
??
4 3
12
123 6183
1836
x
x
xxx
Linear Equations - Solve
Exp: 15 3 9
15 2 9
15 9 2 9 9
6 2
6 2 2
x x
x
x
x
2x
3 x
No fractionsNo parenthesesCombine like terms Use the addition property
Use the multiplication property
Check: 15 = 3x + 9 – x15 (3)(3) + 9 - 3
15 9 + 9 – 315 18 – 3 15 = 15
???
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) = 2 CHECK4x + (-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
23 23 or -3 3
23 -3
23 -3
92 -3
161 3
693
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
Solving Linear Equations
Solving Linear Equations containing decimal numbers.
EXP: CHECK:2.36 0.05 5.21
0.05 2.36 5.21
.95 2.36 5.21
.95 5.21 2.36
.95 2.85
2.85 .95
3
x x
x x
x
x
x
x
x
2.36 0.05 5.21
3 2.36 (0.05)(3) ? 5.21
5.36 0.15 ? 5.21
5.21 5.21
x x
Solving Linear Equations
Solving Linear Equations containing decimal numbers.
EXP # 39: CHECK: 2.3x – 9.34 = 6.3
2.3x – 9.34 = 6.3 2.3(6.8) – 9.34 6.32.3x = 6.3 + 9.34 15.64 – 9.34 6.32.3x = 15.65 6.3 = 6.3x = 15.65/2.3x ≈ 6.8
??
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.
Solving Linear Equations
EXP: 1 1 1 ( 3) 2 ( ) (3) 24 4 4
3 3 2 4 8 2 2 LCD = 4 4 4 4 4 1 4 4
8 3 8 3 4 4 4 4 4
5 5 (4) (4)4 4 4 4
5
x x
x x
x x
x x
x
Solving Linear Equations
EXP: 1 1 4 11 4 11 3 4 11 3 3 3
3312 33 11 33 -11
3
y y y y y y
y y y y
y
Solving Linear Equations
EXP:
1 2 1 1 2 1 LCD= 35 355 7 6 5 7 6
35 70 35 35 35 7 10 3 5 7 6 6 6
-3x 35 1 35 -3 6 3 18
x x x x
x x x x x
x
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
HOMEWORK 2.4
Page 127 - 128
#15, 25, 27, 31, 37, 59, 79, 81