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Linear Inequalities

Linear Inequalities. By Dr. Carol A. Marinas. Solving Linear Equations. PROBLEM x+2 + x = 3 + 1 x 4x x 4 1. Multiply by LCM (4, x, 4x) = 4x 4(x+2) + x = 12 + x 2. Simplify each side 4x + 8 + x = 12 + x 5x + 8 = 12 + x Move terms 4x = 4

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Linear Inequalities

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  1. Linear Inequalities By Dr. Carol A. Marinas

  2. Solving Linear Equations • PROBLEM • x+2 + x = 3 + 1x 4x x 4 • 1. Multiply by LCM (4, x, 4x) = 4x • 4(x+2) + x = 12 + x • 2. Simplify each side • 4x + 8 + x = 12 + x • 5x + 8 = 12 + x • Move terms • 4x = 4 • 4. Divide by 4 • x = 1 • Linear Equations have no exponents higher than 1 and has an EQUAL SIGN. • To solve linear equations • If fractions are involved, multiply by the Least Common Multiples of the denominators. • Simplify each side of the equation • Move the terms so that the variables are on one side and the constants are on the other. • Divide by the coefficient of the variable.

  3. Solving Linear INequalities • Use the same steps as Solving Linear Equations EXCEPT when Multiplying OR Dividing by a negative number you switch the inequality sign. WHY? 4 < 6 If you multiply both sides by –2 – 8 – 12 In order for this to be true, it must be flipped to a > sign. – 8 > – 12

  4. Examples • 3 ( 1 – x ) + 4 > 6 • 3 – 3x + 4 > 6 • –3x + 7 > 6 • –3x > – 1 • x < 1/3 • Any number less than 1/3 will make the original inequality true. • 2x + 4 < 6 • 2x < 2 • x < 1 • This means that all numbers less than and including 1 will make the original inequality true.

  5. Summary Remember: Use the same steps as Solving Linear Equations EXCEPT when Multiplying OR Dividing by a negative number you switch the inequality sign.

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