Question

Which is the best interpretation of the solution set for the compound inequality?

Answer 1

Answer:

  all real numbers

Step-by-step explanation:

Here is the solution to the first inequality:

  3(2x +1) > 21 . . . . . . given

  6x +3 > 21 . . . . . . . . eliminate parentheses

  6x > 18 . . . . . . . . . . .subtract 3

  x > 3 . . . . . . . . . . . . divide by 6

This is all numbers to the right of 3 on the number line.

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The solution to the second inequality is ...

  4x +3 < 3x + 7 . . . . given

  x < 4 . . . . . . . . . . . . subtract 3x+3

This is all numbers to the left of 4 on the number line.

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The conjunction in the system of inequalities is "or", so we are looking for values of x that will satisfy at least one of the conditions. Any value of x will satisfy one or the other or both of these inequalities. The solution is all real numbers.