Solve For $x$.$42=\frac{6}{7} X$Simplify Your Answer As Much As Possible.\$x=$[/tex\]
Understanding the Problem
To solve for x in the equation 42 = (6/7)x, we need to isolate the variable x. This involves getting rid of the fraction and the coefficient of x. We will use algebraic manipulation to simplify the equation and find the value of x.
Step 1: Multiply Both Sides by 7
The first step is to get rid of the fraction by multiplying both sides of the equation by 7. This will eliminate the denominator of the fraction.
42 = (6/7)x
Multiplying both sides by 7:
42 × 7 = (6/7)x × 7
Step 2: Simplify the Equation
Now that we have eliminated the fraction, we can simplify the equation.
42 × 7 = 6x
Step 3: Simplify the Left Side of the Equation
Next, we need to simplify the left side of the equation by multiplying 42 and 7.
42 × 7 = 294
So, the equation becomes:
294 = 6x
Step 4: Divide Both Sides by 6
Now that we have simplified the left side of the equation, we can isolate x by dividing both sides by 6.
294 = 6x
Dividing both sides by 6:
294 ÷ 6 = x
Step 5: Simplify the Right Side of the Equation
Finally, we can simplify the right side of the equation by dividing 294 by 6.
294 ÷ 6 = 49
So, the value of x is:
x = 49
The final answer is .
Understanding the Problem
To solve for x in the equation 42 = (6/7)x, we need to isolate the variable x. This involves getting rid of the fraction and the coefficient of x. We will use algebraic manipulation to simplify the equation and find the value of x.
Q&A
Q: What is the first step to solve for x in the equation 42 = (6/7)x?
A: The first step is to get rid of the fraction by multiplying both sides of the equation by 7.
Q: Why do we multiply both sides of the equation by 7?
A: We multiply both sides of the equation by 7 to eliminate the denominator of the fraction.
Q: What is the result of multiplying 42 by 7?
A: The result of multiplying 42 by 7 is 294.
Q: What is the equation after multiplying both sides by 7?
A: The equation after multiplying both sides by 7 is 294 = 6x.
Q: How do we isolate x in the equation 294 = 6x?
A: We isolate x in the equation 294 = 6x by dividing both sides of the equation by 6.
Q: What is the result of dividing 294 by 6?
A: The result of dividing 294 by 6 is 49.
Q: What is the value of x in the equation 42 = (6/7)x?
A: The value of x in the equation 42 = (6/7)x is 49.
Common Mistakes
- Not multiplying both sides of the equation by 7 to eliminate the fraction.
- Not simplifying the left side of the equation after multiplying both sides by 7.
- Not dividing both sides of the equation by 6 to isolate x.
Tips and Tricks
- Make sure to multiply both sides of the equation by the same number to eliminate the fraction.
- Simplify the left side of the equation after multiplying both sides by 7.
- Divide both sides of the equation by the coefficient of x to isolate x.
Conclusion
Solving for x in the equation 42 = (6/7)x involves getting rid of the fraction and the coefficient of x. We use algebraic manipulation to simplify the equation and find the value of x. By following the steps outlined in this article, you can solve for x in this equation and similar equations.
Frequently Asked Questions
- Q: What is the equation 42 = (6/7)x? A: The equation 42 = (6/7)x is a linear equation where x is the variable.
- Q: How do we solve for x in the equation 42 = (6/7)x? A: We solve for x in the equation 42 = (6/7)x by multiplying both sides of the equation by 7, simplifying the left side of the equation, and dividing both sides of the equation by 6.
- Q: What is the value of x in the equation 42 = (6/7)x? A: The value of x in the equation 42 = (6/7)x is 49.