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Algebra I Recipe: Compound Inequalities
A. Solving a Compound Inequality with “AND”
      **4x + 5 > -7 AND 4x + 5 ≤ 25 is written like -7 < 4x + 5 ≤ 25
  1. Isolate the variable in the middle.
    • Distribute in the middle if possible.
    • Combine like terms in the middle if possible.
    • Add or subtract the number term on each side of both symbols (middle, left, and right).
    • Multiply or divide by the coefficient on each side of both symbols (middle, left, and right).
  2. If the solution contains greater than symbols, rotate the whole solution around to get less than symbols. (This would happen when you multiply or divide by a negative.)
  3. Graph the solution.
    • One of the circles goes on each number in the solution.
    • A darkened bar is graphed between the two circles.
ExamplesExamples:
 –2 < x + 2 ≤ 4
–3 ≥ 2x + 1 ≥ 5
17 < 5 - 3x < 29
B. Solving a Compound Inequality with “OR”
      ** It’s written like 8 + 2x < 6  OR  3x - 2 > 13
  1. Solve each inequality.
  2. The solution must be written with two inequalities connected with “OR”.
  3. Graph each inequality.
    • One of the circles goes on each number in the solution.
    • The darkened bar is graphed in the direction indicated by the symbol with the number.
    • If the darkened bars are going toward each other, the answer is All Real Numbers, so you would graph a darkened bar over the entire number line.
    • If both darkened bars are going to the right, the answer is all number > or ≥ the smallest value.
    • If both darkened bars are going to the left, the answer is all number < or ≤ the largest value.
ExamplesExamples:
3x + 1 < 4  OR   2x - 5 > 7
2x + 1 ≤ 7  OR  -3x - 4 ≤ 2
x - 4 ≥ 3   OR   2x > 18



G Redden

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