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Solve for all values of
y in simplest form.

26=|y-23|
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $26=|y-23|$ $\newline$ Answer: $y=$

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Solve a quadratic equation using square roots

Full solution

Q. Solve for all values of

y

in simplest form.

\newline

26=|y-23|

\newline

Answer:

y=

Set Up Equation: We start by setting up the equation given by the problem. $\newline$ $26 = |y - 23|$ $\newline$ The absolute value equation can be split into two separate equations because if the inside of the absolute value $(y - 23)$ is positive, it will be equal to $26$ , and if it is negative, its opposite $(- (y - 23))$ will be equal to $26$ .
Positive Inside Value: First, we consider the case where the inside of the absolute value is positive. $\newline$ $y - 23 = 26$ $\newline$ Now, we solve for $y$ by adding $23$ to both sides of the equation. $\newline$ $y = 26 + 23$ $\newline$ $y = 49$
Negative Inside Value: Next, we consider the case where the inside of the absolute value is negative. $\newline$ $- (y - 23) = 26$ $\newline$ This simplifies to $y - 23 = -26$ , as the negative sign distributes to make the equation positive. $\newline$ Now, we solve for $y$ by adding $23$ to both sides of the equation. $\newline$ $y = -26 + 23$ $\newline$ $y = -3$

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