<h2><em><u>Answer:</u></em></h2><h2><em><u>First, solve each inequality. I'll solve the first one first.
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>7
</u></em></h2><h2><em><u>≥
</u></em></h2><h2><em><u>2
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>−
</u></em></h2><h2><em><u>5
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>12
</u></em></h2><h2><em><u>≥
</u></em></h2><h2><em><u>2
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>6
</u></em></h2><h2><em><u>≥
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>(
</u></em></h2><h2><em><u>−
</u></em></h2><h2><em><u>∞
</u></em></h2><h2><em><u>,
</u></em></h2><h2><em><u>6
</u></em></h2><h2><em><u>]
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could </u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u> be any number less than 6, but it could also be 6.
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>Let's try the second example:
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>3
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>−
</u></em></h2><h2><em><u>2
</u></em></h2><h2><em><u>4
</u></em></h2><h2><em><u>>
</u></em></h2><h2><em><u>4
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>3
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>−
</u></em></h2><h2><em><u>2
</u></em></h2><h2><em><u>>
</u></em></h2><h2><em><u>16
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>3
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>>
</u></em></h2><h2><em><u>18
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u>>
</u></em></h2><h2><em><u>6
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>(
</u></em></h2><h2><em><u>6
</u></em></h2><h2><em><u>,
</u></em></h2><h2><em><u>∞
</u></em></h2><h2><em><u>)
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either </u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u> is on the interval </u></em></h2><h2><em><u>(
</u></em></h2><h2><em><u>−
</u></em></h2><h2><em><u>∞
</u></em></h2><h2><em><u>,
</u></em></h2><h2><em><u>6
</u></em></h2><h2><em><u>]
</u></em></h2><h2><em><u> or the interval </u></em></h2><h2><em><u>(
</u></em></h2><h2><em><u>6
</u></em></h2><h2><em><u>,
</u></em></h2><h2><em><u>∞
</u></em></h2><h2><em><u>)
</u></em></h2><h2><em><u>. In other words, </u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u> is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that </u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u> could be any real number, since no matter what number </u></em></h2><h2><em><u>x
</u></em></h2><h2><em><u> is, it will fall in one of these intervals. The interval "all real numbers" is written like this:
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>(
</u></em></h2><h2><em><u>−
</u></em></h2><h2><em><u>∞
</u></em></h2><h2><em><u>,
</u></em></h2><h2><em><u>∞
</u></em></h2><h2><em><u>)
</u></em></h2><h2><em><u>
</u></em></h2><h2><em><u>Final Answer</u></em></h2><h2><em><u>Step-by-step explanation:</u></em></h2>
The quality of the goods you produce depends on the quality of your production process. If your production process doesn’t meet the required quality standards, the product may be of inferior quality.
The answer is -30. The absolute value of -3 is 3. Then you evaluate the power of 6 to the power which is 36. Next you multiply the numbers 2 x 3 which is 6. Then calculate the two numbers left over 6 - 36 which is -30.