Q. Solve for all values of y in simplest form.∣∣7y∣∣=5Answer: y=
Absolute Value Equation: We are given the absolute value equation ∣∣7y∣∣=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 ∣∣7y∣∣=5 means that 7y is either 5 or −5.
Case 1: Positive Value: To find the values of y that satisfy the equation, we need to consider both cases: when 7y is 5 and when 7y is −5. Let's first solve for y when 7y is 5.We set up the equation 7y=5.
Solving for y (Case 1): To solve for y, we multiply both sides of the equation by 7 to isolate y.y=5×7y=35
Case 2: Negative Value: Now let's consider the second case, when (y)/(7) is −5. We set up the equation (y)/(7)=−5.
Solving for y (Case 2): Again, to solve for y, we multiply both sides of the equation by 7 to isolate y.y=−5×7y=−35
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