Download 2.1 Solving Linear Equations and Inequalities

2.1 Solving
Linear Equations
and Inequalities
Definitions
• Expression – math phrase that has
operations, numbers and/or variables (no
equals sign). *Simplify*
• Equation – math statement that has 2
expressions that are equal. *Solve*
• Inequality – math statement that compares 2
expressions using <, < , >, > , or ≠. *Solve*
Steps to Solve any
Equation (or Inequality)
1) Simplify each side
Distribute and combine like terms
2) Get the variable only on one side
(add the opposite)
3) Isolate x
Typically, add the opposite and divide
Remember to flip inequality when
multiplying or dividing by a negative!!
Solving Equations
• Ex: 2x – 5 = ­7
• Ex: ½ x + 6 = 1
• Ex: 42 = 7( x – 4)
• Ex: 3(w + 7) ­ 5w = w + 12
Identity
• An equation true for all values of the variable.
• Both sides become exactly the same!
• Ex: 3 (x + 2) = 2x + 5 + x + 1
If you add the last two digits of the year you were born to the age that you will be this year, your answer will be the number 111. Birth Year + ﴾2011 ­ Birth Year﴿ = 2011
Contradiction
• An equation that has no solution.
• It ends up being FALSE!
• Ex:
2x + 7 = 3(x ­ 5) ­ x
Solving (and Graphing)
Inequalities
• When you multiply or divide by a negative, switch the inequality.
• Ex: 2 ­ (x + 2x) > ­7
• Ex: ¼ x ­ 1 < ­2
Homework
YOU DO!!
Page 94 (10­40 even)
Solve and graph.
1) 3(x - 5) > 5x + 9
x < -12
2) -3(x - 4) > 21
x < -3
Solve
3) -4y + 1 = 3y + 1 - 7y
??
Solve
4) 5 - 4c = c + 20
c = -3
5) (r - 3)7 = 6r + 21
r = 42
6) 2(3p + 3) - 9 = 6p
??