Solve the inequality and describe the solution set. y – 6 ≥ 12 y – 6 ≥ 12
First, we will add 6 to both sides of the inequality:
y - 6 + 6 ≥ 12 + 6
Simplifying gives:
y ≥ 18
So the solution set is all real numbers greater than or equal to 18. We can write this as:
{y ∈ ℝ : y ≥ 18} or y ∈ [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 h be the number of hours Gabriella skied. The total cost of skiing can be represented by the equation:
15h + 35 = 95
To solve for h, we first isolate the variable term by subtracting 35 from both sides:
15h = 60
Then, we divide both sides by 15 to solve for h:
h = 4
Therefore, Gabriella skied for 4 hours.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the equation.
c
4
−
5
=
4
To solve this equation, we will first multiply both sides by 4 to eliminate the fraction:
c/4 - 5 = 16
Next, we will add 5 to both sides to isolate the variable term:
c/4 = 21
Finally, we will multiply both sides by 4 to solve for c:
c = 84
Therefore, the solution to the equation is c = 84.
To solve the inequality y - 6 ≥ 12, we need to isolate the variable y on one side of the inequality sign.
Step 1: Start by adding 6 to both sides of the inequality to get rid of the -6 on the left side:
y - 6 + 6 ≥ 12 + 6
Simplifying, we get:
y ≥ 18
Step 2: Now, we have the inequality y ≥ 18. This means that y is greater than or equal to 18. To express the solution set, we can use interval notation or inequality notation.
Interval notation: [18, ∞)
This notation indicates that the solution set includes all values of y starting from 18 and going infinitely to the right.
Inequality notation: y ≥ 18
This notation states that all values of y that are greater than or equal to 18 are part of the solution set.