The solution of the equations or inequalities and express it in interval notation where appropriate. a. −4x−9&lt;11 or 2≤x+1 b. −4x−9&lt;11 and 2≤x+1

Question

The solution of the equations or inequalities and express it in interval notation where appropriate.  a. −4x−9&amp;lt;11 or 2≤x+1  b. −4x−9&amp;lt;11 and 2≤x+1

trisanualb6 · Accepted Answer

Calculation:  a. Solve the inequality −4x−9&amp;lt;11 or 2≤x+1.  −4x−9&amp;lt;11 or 2≤x+1  −4x&amp;lt;20 or x+1≥2  x&amp;gt;−204 or x≥1  x≻5 or x≥1  The solution of the inequality is (−5,∞).  b. Solve the inequality −4x−9&amp;lt;11 or 2≤x+1.  −4x−9&amp;lt;11 and 2≤x+1  −4x&amp;lt;20 and x+1≥2  x&amp;gt;−204 and x≥1  x≻5 and x≥1  The solution of the inequality is [1,∞).  Conclusion:  Hence, the solutions for the equations and inequalities are as follows:  a. The solution of the inequality −4x−9&amp;lt;11 or 2≤x+1 is (−5,∞).  b. The solution of the inequality −4x−9&amp;lt;11 and 2≤x+1 is [1,∞).

Piosellisf · Accepted Answer

Step 1  a) Solve: −4x−9&amp;lt;11 or 2≤x+1  b) −4x−9&amp;lt;11 and 2≤x+1  Possibility 1  −4x−9&amp;lt;11  Add 9 to both sides  −4x−9+9&amp;lt;11+9  −4x&amp;lt;20  Divide both sides by -4  −4x−4&amp;lt;20−4  x≻5  Step 2  Possibility 2  2≤x+1  Flip the equation  x+1≥2  Subtract 1 from both sides  x+1−1≥2−1  x≥1  Answer: x≻5 or x≥1  So, a) (−5, ∞)  b) [1, ∞)

The solution of the equations or inequalities and express it

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