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Manipulate the equation y=5x-11 so that it is written in terms of x. Which equation is equivalent to

A. x=(y/11)-5 B. x=y+11/5 C. y-11/5 D.x=(y/5)+11

1 answer

To manipulate the equation \( y = 5x - 11 \) in order to express \( x \) in terms of \( y \), we can follow these steps:

  1. Start with the original equation: \[ y = 5x - 11 \]

  2. Add 11 to both sides: \[ y + 11 = 5x \]

  3. Divide both sides by 5 to isolate \( x \): \[ x = \frac{y + 11}{5} \]

Now let's rearrange this expression slightly: \[ x = \frac{y}{5} + \frac{11}{5} \]

Now, let's compare this result with the options given:

A. \( x = \frac{y}{11} - 5 \)
B. \( x = \frac{y + 11}{5} \)
C. \( x = \frac{y - 11}{5} \)
D. \( x = \frac{y}{5} + 11 \)

From our manipulation, we see that the correct equivalent equation is: B. \( x = \frac{y + 11}{5} \)