Question

solve the inequality and graph the solution.
\\( \frac{u}{-6} + 7 > 6 \\)
to draw a ray, plot an endpoint and select an arrow. select an endpoint to
change it from closed to open. select the middle of the ray to delete it.
\\(\longleftarrow\\) -10 -8 -6 -4 -2 0 2 4 6 8 10
submit
work it out
not feeling ready yet? these can help:
graph solutions to one-step inequ... (75) solve multi-step inequalities
lesson: solving inequalities lesson: inequalities on a number line

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( u \), we subtract 7 from both sides of the inequality \(\frac{u}{-6}+7 > 6\). This gives us \(\frac{u}{-6}+7 - 7>6 - 7\), which simplifies to \(\frac{u}{-6}>-1\).

Step2: Multiply both sides by -6 (and reverse inequality)

When we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign. So, multiplying both sides of \(\frac{u}{-6}>-1\) by -6, we get \(u < (-1)\times(-6)\). Calculating the right - hand side, we have \(u < 6\).

Answer:

The solution to the inequality \(\frac{u}{-6}+7 > 6\) is \(u < 6\). To graph this solution:

1. On the number line, plot an open circle at \(u = 6\) (since the inequality is strict, \(u\) cannot be equal to 6).
2. Draw an arrow starting from the open circle at 6 and pointing to the left (towards negative infinity) to represent all values of \(u\) that are less than 6.