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Solving one step Inequalities

<. >. <. <. Solving one step Inequalities. <. <. <. >. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to. What do Inequalities mean?.

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Solving one step Inequalities

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  1. < > < < Solving one step Inequalities < < < >

  2. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to

  3. What do Inequalities mean? • A mathematical sentence that uses one of the inequality symbols to state the relationship between two quantities.

  4. Solving an Inequality • Follow the same rules and steps that we used to solve an equation. • Always undo addition or subtraction first, then multiplication or division. • Remember whatever is done to one side of the inequality must be done to the other side. The goal is to get the variable by itself.

  5. Solve x + 8 1 5 - 8 -8 x ≥ 7 • Draw “the river” to separate the inequality into 2 sides • Subtract 8 from both sides • Simplify vertically All numbers greater than 7 (including 7)

  6. -25 -20 -15 -10 -5 0 5 10 15 20 25 You Try r + 16 < -7 • Draw “the river” to separate the inequality into 2 sides • Subtract 16 from both sides • Simplify vertically - 16 -16 r < -23 All numbers less than -23

  7. Solve 7 ≥m - 3 + 3 + 3 10 ≥ m • Draw “the river” to separate the inequality into 2 sides • Add 3 to both sides • Simplify vertically • Put the variable on the left hand side • = m ≤ 10 All numbers less than 10 (including 10)

  8. Solve x - (-2) > 1 • Draw “the river” to separate the inequality into 2 sides • Eliminate the double sign • Subtract 2 from both sides • Simplify vertically x + 2 > 1 - 2 - 2 x > -1 All numbers greater than -1

  9. More Examples 10x > -20 10 10 x > -2 All numbers greater than -2 make this problem true!

  10. There is one special case. • Sometimes you may have to reverse the direction of the inequality sign!! • That only happens when you multiply or divide both sides of the inequality by a negative number.

  11. Solve -5t ≥ 20 -5 -5 t ≥ -4 t ≤ -4 • Draw “the river” to separate the inequality into 2 sides • Divide both sides by -5 • Reverse your inequality sign! All numbers less than -4 (including -4)

  12. -25 -20 -15 -10 -5 0 5 10 15 20 25 Solve ≥ -6 - ≥ -6 ×- x≥15 x ≤ 15 - • Draw “the river” to separate the inequality into 2 sides • Divide both sides by by - 3. Reverse your inequality sign! All numbers less than 15(including 15)

  13. Solve < 2 - < 2 ×- x< -8 x > -8 - • Draw “the river” to separate the inequality into 2 sides • Multiply each side by -4 3. Reverse your inequality sign! All numbers greater than -8

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