Rewrite the equation 4x/3x−12+3=10 in two equations joined by “and.”
The two equations joined by "and" can be:
1) 4x/(3x - 12) + 3 = 10
2) 4x/(3x - 12) + 3 ≠ 10
y = 3 x - 12
4x/y = 7
The two equations joined by "and" can be:
1) y = 3x - 12
2) 4x/y = 7
To rewrite the equation in two separate equations joined by "and," we need to isolate the terms on either side of the equation. Let's break down the steps:
Step 1: Start with the given equation:
4x/(3x - 12) + 3 = 10
Step 2: Subtract 3 from both sides to isolate the fraction term on the left side:
4x/(3x - 12) = 10 - 3
4x/(3x - 12) = 7
Step 3: Cross-multiply to eliminate the fraction:
4x = 7(3x - 12)
Step 4: Distribute the 7 on the right side:
4x = 21x - 84
Step 5: Move all terms involving x to one side by subtracting 21x from both sides:
4x - 21x = -84
-17x = -84
Step 6: Divide both sides by -17 to solve for x:
x = -84 / -17
x ≈ 4.94 (rounded to two decimal places)
Now, to rewrite the equation in two equations joined by "and":
Equation 1: 4x/(3x - 12) + 3 = 10
Equation 2: x = 4.94
These two equations represent the given equation, where Equation 1 encapsulates the original equation, and Equation 2 provides the solution for x.