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QuestionSolve and graph the inequality 5(b−6)≥105(b-6) \geq 10. Plot endpoints, change one to open, and delete the middle section.

Studdy Solution

STEP 1

Assumptions1. The inequality to solve is 5(b−6)≥105(b-6) \geq10 . We need to find the value of bb that satisfies the inequality3. The inequality is linear, meaning it involves a variable to the first power4. The solution will be a range of values, not a single value

STEP 2

First, we need to simplify the left side of the inequality. We can do this by distributing the5 to both terms inside the parentheses.
5(b−6)=5b−305(b-6) =5b -30So, the inequality becomes5b−30≥105b -30 \geq10

STEP 3

Next, we need to isolate the variable bb on one side of the inequality. We can do this by adding30 to both sides of the inequality.
5b−30+30≥10+305b -30 +30 \geq10 +30This simplifies to5b≥405b \geq40

STEP 4

Finally, to solve for bb, we need to divide both sides of the inequality by.
b≥40\frac{b}{} \geq \frac{40}{}This simplifies tob≥8b \geq8

STEP 5

Now that we have the solution to the inequality, we can graph it. Since bb is greater than or equal to8, we will draw a closed circle at8 (indicating that8 is included in the solution) and draw a line extending to the right (indicating all numbers greater than8).
So, the solution to the inequality 5(b−)≥105(b-) \geq10 is b≥8b \geq8.

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