Solve for b, then find the value of b when a = 3.
4a = 2b − 7
(1 point)
Responses
–nine-halves
– Image with alt text: nine-halves
five-halves
Image with alt text: five-halves
nineteen-halves
Image with alt text: nineteen-halves
17
To solve for b, we need to isolate it on one side of the equation.
Given equation:
4a = 2b - 7
First, let's add 7 to both sides to eliminate the -7:
4a + 7 = 2b
Next, let's divide both sides by 2 to solve for b:
(4a + 7) / 2 = b
Simplifying further:
2a + 3.5 = b
Therefore, the value of b when a = 3 is:
2(3) + 3.5 = b
6 + 3.5 = b
9.5 = b
So, the correct answer is: nineteen-halves (9.5)
To solve for b, we need to isolate it on one side of the equation. Let's begin by getting rid of the 2 by dividing both sides of the equation by 2:
4a = 2b - 7
(4a)/2 = (2b - 7)/2
2a = b - (7/2)
Now, let's isolate b by adding (7/2) to both sides of the equation:
2a + (7/2) = b
So, the value of b in terms of a is b = 2a + (7/2).
To find the value of b when a = 3, substitute a = 3 into the equation:
b = 2(3) + (7/2)
b = 6 + (7/2)
To simplify, add the fractions:
b = 6 + (7/2)
b = (12/2) + (7/2)
b = 19/2
Therefore, when a = 3, the value of b is 19/2 or nineteen-halves.