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Solve for all values of 
y in simplest form.

|(y)/(7)|=5
Answer: 
y=

Solve for all values of y y in simplest form.\newliney7=5 \left|\frac{y}{7}\right|=5 \newlineAnswer: y= y=

Full solution

Q. Solve for all values of y y in simplest form.\newliney7=5 \left|\frac{y}{7}\right|=5 \newlineAnswer: y= y=
  1. Absolute Value Equation: We are given the absolute value equation y7=5\left|\frac{y}{7}\right|=5. The absolute value of a number is the distance of that number from zero on the number line, which means it is always non-negative. Therefore, the equation y7=5\left|\frac{y}{7}\right|=5 means that y7\frac{y}{7} is either 55 or 5-5.
  2. Case 11: Positive Value: To find the values of yy that satisfy the equation, we need to consider both cases: when y7\frac{y}{7} is 55 and when y7\frac{y}{7} is 5-5. Let's first solve for yy when y7\frac{y}{7} is 55.\newlineWe set up the equation y7=5\frac{y}{7} = 5.
  3. Solving for y (Case 11): To solve for y, we multiply both sides of the equation by 77 to isolate yy.\newliney=5×7y = 5 \times 7\newliney=35y = 35
  4. Case 22: Negative Value: Now let's consider the second case, when (y)/(7)(y)/(7) is 5-5. We set up the equation (y)/(7)=5(y)/(7) = -5.
  5. Solving for yy (Case 22): Again, to solve for yy, we multiply both sides of the equation by 77 to isolate yy.y=5×7y = -5 \times 7y=35y = -35

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