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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 ??