Solve the inequality and describe the solution set.
y – 6 ≥ 12.
the answer is 18 but explain why
To solve the inequality, we want to isolate the variable y on one side of the inequality symbol. We can do this by adding 6 to both sides of the inequality:
y - 6 + 6 ≥ 12 + 6
Simplifying, we get:
y ≥ 18
This means that any value of y that is greater than or equal to 18 will make the inequality true. The solution set is therefore:
{y | y ≥ 18}
This can also be written as [18, ∞) in interval notation, meaning that the solution set consists of all numbers from 18 and infinitely upward on the number line.
Therefore, 18 is a part of the solution set, but it is not the answer to the inequality. The answer is all numbers greater than or equal to 18.
Gabriella went skiing. She paid $35 to rent skis and $15 an hour to ski. If she paid a total of $95, how many hours did she ski? Write an algebraic equation to represent the situation and solve it.
Let x be the number of hours Gabriella skied. The total cost of skiing is the sum of the cost of renting skis and the cost of skiing for x hours.
Algebraic equation:
35 + 15x = 95
To solve for x, we can first isolate the variable by subtracting 35 from both sides of the equation:
15x = 60
Then, we can solve for x by dividing both sides by 15:
x = 4
Therefore, Gabriella skied for 4 hours.
To solve the inequality y - 6 ≥ 12, we can isolate the variable y by adding 6 to both sides of the inequality:
y - 6 + 6 ≥ 12 + 6
y ≥ 18
The solution set for this inequality is all values of y that are greater than or equal to 18. This means that any value of y that is 18 or greater would make the inequality true.