Four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x.
A. x ≥ 26
B. x ≥ –15
C. x ≥ 15
D. x ≥ –26
4(x+15) ≥ 120
4x + 60 ≥ 120
4x ≥ 60
x ≥ 15
Let's solve the equation step by step:
Given: Four times the sum of a number and 15 is at least 120.
Step 1: Translate the given sentence into an equation:
4(x + 15) ≥ 120
Step 2: Distribute the 4 across the parentheses:
4x + 60 ≥ 120
Step 3: Subtract 60 from both sides of the inequality to isolate the variable:
4x ≥ 60
Step 4: Divide both sides of the inequality by 4 to solve for x:
x ≥ 15
Therefore, the correct answer is C. x ≥ 15.
To find all possible values for x, we need to solve the given inequality:
4(x + 15) ≥ 120
First, we distribute the 4 to both terms inside the parentheses:
4x + 60 ≥ 120
Next, we isolate the variable by subtracting 60 from both sides of the inequality:
4x ≥ 120 - 60
Simplifying further:
4x ≥ 60
Finally, we divide both sides of the inequality by 4 to solve for x:
x ≥ 60/4
Simplifying:
x ≥ 15
Therefore, the correct answer is:
C. x ≥ 15