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What value makes the equation −5=4−3x/4−3x undefined

Responses:

−3/4

−4/3

3/4

4/3

5 answers

To determine when the equation \(-5 = \frac{4 - 3x}{4 - 3x}\) becomes undefined, we need to look at the denominator of the fraction. The expression \(\frac{4 - 3x}{4 - 3x}\) will be undefined when the denominator equals zero, which occurs when:

\[ 4 - 3x = 0 \]

Solving for \(x\):

\[ 4 = 3x \] \[ x = \frac{4}{3} \]

Thus, the value that makes the equation undefined is \(\frac{4}{3}\).

So the correct response is:

4/3

Solve the equation for the variable k: 30/k+1=4.(1 point)
Responses

6

1/6

10

1/10

To solve the equation:

\[ \frac{30}{k} + 1 = 4 \]

first, we'll isolate the term containing \(k\):

  1. Subtract 1 from both sides:

\[ \frac{30}{k} = 4 - 1 \]

\[ \frac{30}{k} = 3 \]

  1. Next, we can cross-multiply to eliminate the fraction:

\[ 30 = 3k \]

  1. Now, divide both sides by 3 to solve for \(k\):

\[ k = \frac{30}{3} = 10 \]

Thus, the solution for \(k\) is:

10

What is the value for the variable f in 17/3f−1=1 ?(1 point)
Responses

6

4

3

5

To solve the equation

\[ \frac{17}{3f} - 1 = 1 \]

we will first isolate the term containing \(f\).

  1. Add 1 to both sides:

\[ \frac{17}{3f} = 1 + 1 \]

\[ \frac{17}{3f} = 2 \]

  1. Now, cross-multiply to get rid of the fraction:

\[ 17 = 2 \cdot 3f \]

  1. This simplifies to:

\[ 17 = 6f \]

  1. Next, solve for \(f\) by dividing both sides by 6:

\[ f = \frac{17}{6} \]

Since \(\frac{17}{6}\) is not one of the provided options, it appears I have made a mistake in interpreting your options. Let's double-check the original equation and steps:

The original equation was \( \frac{17}{3f} - 1 = 1 \):

Rearranging gives: \[ \frac{17}{3f} = 2 \Rightarrow 17 = 2 \cdot 3f \Rightarrow 17 = 6f \Rightarrow f = \frac{17}{6} \]

This confirms that the value of \(f\) is \(\frac{17}{6}\). However, since none of the response options match, I suspect there may be an error or miscommunication in the provided choices or the equation itself.

Please double-check to confirm the equation or options provided so I can assist you further!