rewrite the equation 6/x-2 = 3 as two equations joined by and

Answer 1

To rewrite the equation \( \frac{6}{x} - 2 = 3 \) as two equations joined by "and," we first isolate \( \frac{6}{x} \).

Starting with the original equation: \[ \frac{6}{x} - 2 = 3 \]

We add 2 to both sides: \[ \frac{6}{x} = 5 \]

Now we can express this as two separate equations. The first equation represents the equation we derived: \[ \frac{6}{x} = 5 \]

The second part comes from recognizing that the variable \( x \) cannot be zero (since division by zero is undefined): \[ x \neq 0 \]

So, we can rewrite the original equation as: \[ \frac{6}{x} = 5 \quad \text{and} \quad x \neq 0 \]

Answer 2

rewrite the equation {6}/{x-2} = 3 as two equations joined by and

Answer 3

To rewrite the equation \(\frac{6}{x-2} = 3\) as two equations joined by "and," we first manipulate the equation.

Starting with: \[ \frac{6}{x-2} = 3 \]

We can isolate \(6\) by multiplying both sides by \(x - 2\): \[ 6 = 3(x - 2) \]

Now, let's distribute the \(3\): \[ 6 = 3x - 6 \]

Next, we can rearrange it to find \(x\): \[ 3x - 6 = 6 \quad \text{or} \quad 3x = 12 \quad \text{or} \quad x = 4 \]

Now, we note that we must also consider the restriction imposed by the original equation—specifically, that the denominator cannot be zero: \[ x - 2 \neq 0 \quad \Rightarrow \quad x \neq 2 \]

Thus, we can write the original equation as two equations joined by "and": \[ x = 4 \quad \text{and} \quad x \neq 2 \]

This represents the solution while enforcing the restriction on \(x\).

Answer 4

solve the equation and write the answer using set notation.
{12}/{x-4} =2 and x≠4

Answer 5

To solve the equation

\[ \frac{12}{x-4} = 2 \]

we first isolate the variable \(x\). Start by multiplying both sides by \(x - 4\) (keeping in mind that \(x \neq 4\) to avoid division by zero):

\[ 12 = 2(x - 4) \]

Next, distribute the \(2\):

\[ 12 = 2x - 8 \]

Now, add \(8\) to both sides:

\[ 12 + 8 = 2x \]

This simplifies to:

\[ 20 = 2x \]

Now, divide both sides by \(2\):

\[ x = 10 \]

Since we also have the condition \(x \neq 4\), we see that \(x = 10\) satisfies this condition.

Now, we can express the solution in set notation. The solution set is:

\[ {10} \]

Answer 6

rearrange the formula t=d/v to highlight d

Answer 7

To rearrange the formula \( t = \frac{d}{v} \) to highlight \( d \), you can follow these steps:

1. Start with the original equation: \[ t = \frac{d}{v} \]

2. Multiply both sides by \( v \) to isolate \( d \): \[ d = t \cdot v \]

Now, the formula highlighted for \( d \) is: \[ d = t \cdot v \]