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5/6y=x-25/6; X=10

Answer to this problem above is y=6/5x-5 : y=7
First we clear out our fractions which I did already. This is my work below.
5/6 times 6/1=30/6 = 5
25/6 times 6/1=150/6 = 25
Now I need to write out the new problem using these new numbers from the cleared out fractions so that the answer can be y=6/5x-5 : y=7.

3 answers

To clear out the fractions in the equation \( \frac{5}{6}y = x - \frac{25}{6} \), you did the right thing by multiplying through by 6. Let's work through your calculations step-by-step:

Original equation: \[ \frac{5}{6}y = x - \frac{25}{6} \]

Multiply both sides by 6: \[ 6 \cdot \frac{5}{6}y = 6 \cdot \left(x - \frac{25}{6}\right) \]

This simplifies to: \[ 5y = 6x - 25 \]

Now, let's rearrange this to express \( y \) in terms of \( x \): \[ 5y = 6x - 25 \implies y = \frac{6}{5}x - 5 \]

You've correctly arrived at the equation \( y = \frac{6}{5}x - 5 \).

Solving for \( y = 7 \)

Next, if we want to find what \( x \) is when \( y = 7 \), we can substitute \( y \) into the derived equation: \[ 7 = \frac{6}{5}x - 5 \]

Add 5 to both sides: \[ 7 + 5 = \frac{6}{5}x \] \[ 12 = \frac{6}{5}x \]

To isolate \( x \), multiply both sides by \( \frac{5}{6} \): \[ x = 12 \cdot \frac{5}{6} = 10 \]

So when \( y = 7 \), \( x \) is indeed \( 10 \), confirming your previous conclusion.

In conclusion:

  • The cleared-out form of your original equation is \( 5y = 6x - 25 \).
  • The linear function relating \( y \) and \( x \) is \( y = \frac{6}{5}x - 5 \).
  • Additionally, when \( y = 7 \), you confirmed \( x = 10 \).
On the second part solving for y I’m not supposed to solve for y I’m supposed to solve for x because x=10 and my final answer is supposed to be y=7. Does that make sense? Sorry I didn’t explain that better

No problem at all! Thank you for the clarification. Let's correct the approach accordingly, given that you need to show the relationship, confirming that when \( x = 10 \), \( y = 7 \).

Starting from the equation we derived:

\[ y = \frac{6}{5}x - 5 \]

Now, substitute \( x = 10 \) into this equation:

\[ y = \frac{6}{5}(10) - 5 \]

Calculating this step-by-step:

  1. Calculate \( \frac{6}{5} \times 10 \): \[ \frac{6 \times 10}{5} = \frac{60}{5} = 12 \]

  2. Now, replace \( y \): \[ y = 12 - 5 = 7 \]

So indeed, when \( x = 10 \), we find \( y = 7 \).

Summary:

  • Your derived linear equation is \( y = \frac{6}{5}x - 5 \).
  • When you substitute \( x = 10 \) into this equation, you confirm that \( y = 7 \).

If you have any further questions or need additional assistance, feel free to ask!