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Solving and Graphing Linear Inequalities

Learn about solving and graphing linear inequalities, including one-step inequalities. Discover how to interpret symbols and graph solutions accurately. Practice graphing and solving with helpful examples.

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Solving and Graphing Linear Inequalities

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  1. Solving and Graphing Linear Inequalities Solving One-Step Linear Inequalities

  2. What’s an inequality? • Is a range of values, rather than ONE set number. YOU SOLVE IT PRETENDING THERE IS AN EQUAL SIGN. However, there is an extra step to show an answer.

  3. Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO

  4. How to graph the solutions > Graph any number greater than. . . open circle, line to the right < Graph any number less than. . . open circle, line to the left Graph any number greater than or equal to. . . closed circle, line to the right Graph any number less than or equal to. . . closed circle, line to the left

  5. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solutions…. You can have a range of answers…… All real numbers less than 2 x< 2

  6. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solutions continued… All real numbers greater than -2 x > -2

  7. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solutions continued…. All real numbers less than or equal to 1

  8. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solutions continued… All real numbers greater than or equal to -3

  9. Did you notice, -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Some of the dots were solid and some were open? Why is that? If the symbol is > or < then dot is open because it can not be equal. If the symbol is  or  then the dot is solid, because it can be that point too.

  10. Practice Graphing Here

  11. -5 -4 -3 -2 -1 0 1 2 3 4 5 Write and Graph a Linear Inequality Sue loves sweets. She will have more than 1 cookie this holiday season!

  12. -5 -4 -3 -2 -1 0 1 2 3 4 5 Write and Graph a Linear Inequality Joe is on a diet. He gained less than 2 pounds during Thanksgiving. He might have even lost weight!

  13. +3 +3 Solving an Inequality Solving a linear inequality in one variable is much like solving a linear equation in one variable. Remember the party! x – 3 < 5 Add the same number to EACH side. x < 8 Graph the Solution

  14. -6 -6 Solve Subtract the same number from EACH side. Graph the Solution

  15. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solve Graph the solution.

  16. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solve Graph the solution. THERE IS A TRICK!

  17. Practice One-Step Solving with Addition and Subtraction

  18. THE TRAP….. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement.

  19. (2) (2) Solving using Multiplication Multiply each side by the same positive number.

  20. 3 3 Solving Using Division Divide each side by the same positive number.

  21. (-1) (-1) See the switch Solving by multiplication of a negative # Multiply each side by the same negative number and REVERSE the inequality symbol. Multiply by (-1).

  22. -2 -2 Solving by dividing by a negative # Divide each side by the same negative number and reverse the inequality symbol.

  23. Homework Page 337 – 338 # 22-54 evens 55-60 61 & 65

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