Rewrite the equation 5/b=10 as two equations joined by “and
5/b = 10 can be rewritten as:
5/b = 10 and b ≠ 0
What value will complete the set of equations (15/3x−9)−4=12 and x≠ _____?
To complete the set of equations (15/3x−9)−4=12 and x≠ _____, we need to find the value of x that makes the equations be true.
Let's solve the first equation:
(15/3x−9)−4 = 12
We can simplify the equation by first simplifying the fraction:
5/x - 3 = 12 (divided 15 by 3x, and -9 by 3)
5/x = 12 + 3 (added 3 to both sides)
5/x = 15
Next, we can cross-multiply and solve for x:
5 = 15x
x = 5/15
x = 1/3
Therefore, x ≠ 1/3.
No its not
Apologies for the confusion. Let's solve the equation correctly this time.
The given equation is (15/3x−9)−4=12.
First, let's simplify the left side of the equation:
(15/3x−9)−4 = 12
(5/x - 9) - 4 = 12 (divided 15 by 3x)
5/x - 13 = 12 (combined like terms)
Next, let's isolate the fraction term:
5/x = 12 + 13
5/x = 25
Now, let's cross-multiply and solve for x:
5x = 25
x = 25/5
x = 5
Hence, the value that completes the equation is x = 5. Therefore, x ≠ 5.
To rewrite the equation 5/b = 10 as two equations joined by "and," we need to break it down into two separate equations.
Equation 1: 5/b = 10
Equation 2: b ≠ 0
Therefore, the two equations joined by "and" would be:
1) 5/b = 10, and
2) b ≠ 0.
To rewrite the equation 5/b = 10 as two equations joined by "and," we need to consider the two possible solutions: b = 5/10 and b = -5/10.
1. First, let's consider b = 5/10:
- We can multiply both sides of the equation by b (since b ≠ 0), which gives us: 5 = 10b.
- Dividing both sides of the equation by 10, we get: 5/10 = b.
- Simplifying the right side of the equation, we have: 1/2 = b.
2. Now, let's consider b = -5/10:
- Again, we can multiply both sides of the equation by b (since b ≠ 0), which gives us: 5 = -10b.
- Dividing both sides of the equation by -10, we get: 5/-10 = b.
- Simplifying the right side of the equation, we have: -1/2 = b.
Therefore, the equation 5/b = 10 can be represented by two equations joined by "and": b = 1/2 and b = -1/2.