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1. Solve 3x + 2 ≤ -7 x ≤ 3 x ≤ -3 x ≥ 3 x ≥ -3 Now, let's talk about interval notation... x > 2 can be written as (2, ∞) 2 it's like the open dot because 2 is not a solution infinity always is paired with parentheses because the infinity is not a # Remember, when you divide both sides by a negative number or multiply both sides by the same negative number, you must flip the sign! < becomes > > becomes < ≤ becomes ≥ ≥ becomes ≤ 2. Solve 6 - x > 8 x < -2 x < 2 x > -2 x > 2 In interval notation, the solution is (-2, ∞) (-∞, -2) (2, ∞) (-∞, 2) 3. Solve 2(x - 3) > -4 x > 5 x > -5 x > -1 x > 1 Interval notation (-∞, 5) (-∞, 1) (1, ∞) (-1, ∞) 4. Solve -3x + 7x > 20 x > 2 x > 5 x < -5 x > -5 (2, ∞) (5, ∞) (-∞, -5) (-5, ∞) In interval notation 5. Solve 4 - 2(x - 1) < -8 x < -3 x > 7 x > -5 x < 7 (-∞, -3) (-∞, 7) (7, ∞) (-5, ∞) In interval notation 6. Solve-x - 9 < -5 x < 4 x < -4 x > 4 x > -4 (-∞, 4) (-∞, -4) (-4, ∞) (-∞, ∞) In interval notation Negative infinity is always on the left Positive infinity is always on the right In interval notation, (-∞, ∞) means... All real numbers! (-∞, 3) (5, ∞) 7. Solve6x + 2 > 4x - 8 x > 5 x > -5 x > 3 x > -3 In interval notation, if the solution includes (is equal to) a number, you must use brackets. it's like the closed dot on the graph [3, 5] The solution includes 3 and 5 - ∞ Left Remember that you must read a graph from left to right even though the arrows make it look like we start somewhere in the middle and read in both directions. Infinity always gets parentheses! to right ∞ In interval notation, this would look like -5 [-5, 2] -5 ≤ x ≤ 2 0 I think that interval notation is easier; what do you think? 2 (set notation) 8. Solve x + 3 ≤ -7 - 4x x ≤ 1 x ≥ 2 x ≤ 2 x ≤ -2 [1, ∞) (-∞, -2] [1, 2] (-∞, 2] Interval Notation 9. Solve2(x + 11) > -3(x + 1) x > -5 x < 5 x < -5 x > 5 10. Solve -3 + x ≥ 4 x ≥ 2 x ≤ -14 x ≥ 14 x ≥ -12 2 |