Considering the one-time deposit and monthly rent, the equation c = 20m + 25 can be used to represent the total cost of a gym membership for m months. What is the amount of the sign-up fee?
The sign-up fee is represented by the number 25 in the equation.
Apologies for the confusion. The correct equivalent equation to 2x - 4a = 10 is:
x = 5 + 2a
The property illustrated by the equation "pi x 3 = 3 x pi" is the commutative property of multiplication.
The algebraic expression that models the word phrase "6 times the sum of a and b" is 6(a + b).
The algebraic expression that describes the situation is: 3d + 305.
To solve the equation for t, we need to isolate t on one side of the equation. Here's the step-by-step process:
Step 1: Divide both sides of the equation by 3r^4:
S/(3r^4) = t
Therefore, the equation, S = 3r^4t, when solved for t, is t = S/(3r^4).
The inequality that represents the sentence "Seven fewer than a number is at least 14" is:
x - 7 ≥ 14
To solve the given absolute value equation |4x - 1| = 1, we can break it down into two separate equations:
1) 4x - 1 = 1
2) 4x - 1 = -1
Solving Equation 1:
4x - 1 = 1
Adding 1 to both sides:
4x = 2
Dividing by 4:
x = 1/2
Solving Equation 2:
4x - 1 = -1
Adding 1 to both sides:
4x = 0
Dividing by 4:
x = 0
So, the solution to the absolute value equation |4x - 1| = 1 is x = 1/2 and x = 0.
To solve the inequality |2x + 7| ≤ 27, we need to consider both possibilities when the expression inside the absolute value is positive or negative.
Case 1: 2x + 7 ≥ 0
When 2x + 7 ≥ 0, the absolute value can be removed, so we have:
2x + 7 ≤ 27
Subtracting 7 from both sides:
2x ≤ 20
Dividing both sides by 2:
x ≤ 10
Case 2: 2x + 7 < 0
When 2x + 7 < 0, the absolute value becomes -1 times the expression inside:
-(2x + 7) ≤ 27
-2x - 7 ≤ 27
Subtracting 7 from both sides:
-2x ≤ 34
Dividing both sides by -2 (and reversing the inequality):
x ≥ -17
Combining the two cases, the solution to the inequality |2x + 7| ≤ 27 is -17 ≤ x ≤ 10.
Now, let's graph the solution on a number line:
------------------●-------------●------------------
-17 10
The solid dots represent the values -17 and 10, which are included in the solution. The line segment between them represents the values of x that satisfy the inequality.