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Inequalities

Inequalities. Inequalities. Show that two or more expressions are NOT equal by using <, >, ≤, or ≥. Solving Inequalities. Inequalities are solved exactly the same way that equations are solved.

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Inequalities

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  1. Inequalities

  2. Inequalities • Show that two or more expressions are NOT equal by using <, >, ≤, or ≥.

  3. Solving Inequalities • Inequalities are solved exactly the same way that equations are solved. • To solve an inequality, you must get the variable alone on one side of the inequality sign (<, >). To do this, you must get rid of any other numbers by performing the opposite function. BUT whatever you do to one side, you must do to the other.

  4. Inequality Example • X + 3 > 6 • We need to get x by itself so we get rid of 3 by subtracting (opposite of addition) - BUT what we do to one side we must do to the other • X + 3 - 3 > 6 - 3 • This leaves x > 3

  5. Inequality Example • Ex: n - 7 ≤ 3 • We want the n by itself so we have to get rid of the 7 so we add (opposite of subtraction) 7 BUT what we do to one side we must do to the other • N - 7 + 7 ≤ 3 + 7 • N ≤ 10

  6. Inequality Example • EX: 3n > 12 • We want n by itself so we must get rid of the 3. 3n means 3 times n so we have to do the opposite function - divide. BUT what we do to one side, we must do to the other • 3n ÷ 3 > 12 ÷ 3 • N > 4

  7. Inequality Example • Ex: n ⁄ 4 < 5 • We have to get n by itself. N and 4 are divided so we do the opposite - multiply BUT what we do to one side we must do to the other. • N ⁄ 4 x 4 < 5 x 4 • N < 20

  8. Inequalities • Very Important Note: • If you MULTIPLY or DIVIDE by a NEGATIVE number, you must switch the direction of the inequality sign

  9. Inequality Example • EX: - 3n > 12 • We want n by itself so we must get rid of the 3. 3n means 3 times n so we have to do the opposite function - divide. BUT what we do to one side, we must do to the other • -3n ÷ -3 > 12 ÷ -3 • SWITCH DIRECTION OF INEQUALITY SIGN • N < - 4

  10. Graphing Inequalities

  11. Graphing Inequalities • First, find the answer on the number line. If the variable can be equal to the answer (≤ or ≥) then fill in the circle. If not (< or >), then leave the circle open. • If the variable is less than the answer, shade to the left of the circle • If the variable is more than the answer, shade to the right of the circle.

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