0.1/0.6 = 2/x =x/24
Is there a question in there?
As it stands, the two equalities are inconsistent.
To solve the equations 0.1/0.6 = 2/x = x/24, we will break it down step by step.
Step 1: Simplify the first equation: 0.1/0.6 = 1/6
Step 2: Simplify the second equation: 2/x = 1/6
Step 3: Solve for x in the second equation by cross multiplying: 6 * 2 = x * 1
Step 4: Simplify: 12 = x
Step 5: The value of x in the equation 2/x is 12.
Step 6: Substitute the value of x in the third equation: x/24 becomes 12/24.
Step 7: Simplify 12/24: Divide both the numerator and denominator by their greatest common divisor, which is 12. 12 ÷ 12 = 1, and 24 ÷ 12 = 2. Therefore, 12/24 simplifies to 1/2.
Step 8: The value of x in the equation x/24 is 1/2.
To solve the equations \(0.1/0.6 = 2/x\) and \(2/x = x/24\), we can use a method called cross-multiplication.
First, let's focus on the equation \(0.1/0.6 = 2/x\):
1. Multiply both sides of the equation by \(0.6\) to eliminate the denominator. This gives us \(0.1 = (2/x) \times 0.6\).
2. Simplify the right side of the equation by multiplying \(2\) and \(0.6\), resulting in \(0.1 = 1.2/x\).
3. Multiply both sides of the equation by \(x\) to isolate the variable. This gives us \(0.1x = 1.2\).
4. Divide both sides of the equation by \(0.1\) to solve for \(x\). We get \(x = 1.2/0.1\).
5. Simplify the right side by dividing \(1.2\) by \(0.1\). The final solution is \(x = 12\).
Now let's move on to the second equation \(2/x = x/24\):
1. Multiply both sides of the equation by \(x\) to eliminate the denominator. This gives us \(2 = (x/24) \times x\).
2. Simplify the right side of the equation by multiplying \(x\) and \(x\), resulting in \(2 = x^2/24\).
3. Multiply both sides of the equation by \(24\) to isolate the variable. This gives us \(48 = x^2\).
4. Take the square root of both sides of the equation to solve for \(x\). We have \(x = \sqrt{48}\).
5. Simplify the square root of \(48\). It is important to note that square roots have both a positive (\(\sqrt{48}\)) and negative (\(-\sqrt{48}\)) solution. In this case, we are assuming we are looking for the positive solution, so \(x \approx 6.93\).
Therefore, the solutions to the equations \(0.1/0.6 = 2/x\) and \(2/x = x/24\) are \(x = 12\) and \(x \approx 6.93\), respectively.