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Solving and Graphing one step Inequalities

Solving One-Step Inequalities. Solving and Graphing one step Inequalities. What’s an inequality?. An algebraic relation that has variables, numbers, operations and symbols. Also shows that a quantity is greater than or less than another quantity.

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Solving and Graphing one step Inequalities

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  1. Solving One-Step Inequalities Solving and Graphing one step Inequalities

  2. What’s an inequality? An algebraic relation that has variables, numbers, operations and symbols. Also shows that a quantity is greater than or less than another quantity. Is a set with several solutions, rather than ONE solution Speed limit

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

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

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

  6. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solutions continued…. All numbers less than or equal to 1

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

  8. 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 do you think that is? If the symbol is > or < then dot is open because it can not be that point. If the symbol is  or  then the dot is solid, because it can be that point too.

  9. +3 +3 Solving an Inequality Solving an inequality in one variable is much like solving an equation in one variable. Isolate the variable on one side adding the opposite. Solve using addition: x – 3 < 5 Addthe opposite number to EACH side. x < 8 All numbers smaller than 8

  10. -6 -6 Solving Using Subtraction Add the opposite number to EACH side. All numbers greater or equal than 4

  11. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving addition… Isolate the variable. Graph the solution. -5 -5 x  -2 All numbers greater or equal than -2 Add the opposite number to EACH side.

  12. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving addition… Isolate the variable. Graph the solution. -6 -6 m < -4 All numbers smaller than -4 Add the opposite number to EACH side.

  13. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving Subtraction… Isolate the variable. Graph the solution. + 4 +4 n  2 All numbers greater or equal than 2 Add the opposite number to EACH side.

  14. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving Subtraction… Isolate the variable. Graph the solution. + 3 +3 n < 5 All numbers smaller than 5 Add the opposite number to EACH side.

  15. Solve and graph the following inequalities: 0 -6 -15 0 -9 0 -4 -3 0 -8 2 0 0 0 12 10 0 0 19 0 6) y +(-5) < 5 1) x > 2 2) x  -3 7) f + 8  -7 3) X + 5  -3 8) 12 –(-p) > 6 4) X –(-2) < -7 9) p +(-8)  11 5) -2 + m > 10 10) 2k +12  4

  16. 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.  <  >  < > 

  17. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving Multiplication Isolate the variable. 2 w < 8 2 2 < 4 Do the opposite on each side All numbers smaller than 4

  18. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving Multiplication Isolate the variable. -5 k   15 -5 -5 Since you divide by a negative each side, flip the symbol  - 3 Do the opposite on each side All numbers greater or equal to -3

  19. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving Division Do the opposite on each side Isolate the variable. J J ( 3 )   ( 3 ) 1 3 3 All numbers greater or equal than 3

  20. -5 -4 -3 -2 -1 0 1 2 3 4 5 Solving Division Do the opposite on each side Isolate the variable. b b ( -2 ) < < ( -2 ) 2 -2 Since you multiply by a negative each side, flip the symbol  -4 All numbers greater than -4

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

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

  23. Time for practice:solve and graph the following inequalities 0 -12 -1 -4 -5 0 0 6 0 0 0 0 18 2 0 1 a  18 5) a /3  6 1) 3 H  6 H  2 p  -12 6) p/4  -3 2) 2y  -8 y  -4 L  6 7) L/-3  -2 3) -6 K  6 K  -1 g  -5 8) g/-5  1 m  1 4) -5 m  -5

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