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Understanding Inequalities in Math

Learn how to show expressions are not equal and solve inequalities step by step with examples and important notes on switching inequality signs. Also, understand graphing inequalities on number lines.

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Understanding Inequalities in Math

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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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