Solve for all values of y in simplest form. 11=|y-22| Answer: y=

Given Equation: We are given the equation 11 = |y - 22|. The absolute value equation can have two possible cases: either the expression inside the absolute value is positive or it is negative. We will consider both cases to find all possible values of y.Case 1: Case 1: The expression inside the absolute value is non-negative, which means y - 22 is greater than or equal to 0. We can remove the absolute value bars and solve for y. 11 = y - 22 Now, we add 22 to both sides of the equation to solve for y. 11 + 22 = y - 22 + 22 33 = y So, one possible value of y is 33.Case 2: Case 2: The expression inside the absolute value is negative, which means y - 22 is less than 0. In this case, we need to consider the opposite of the expression inside the absolute value to be equal to 11. 11 = -(y - 22) Now, we distribute the negative sign inside the parentheses. 11 = -y + 22 Next, we subtract 22 from both sides of the equation to solve for y. 11 - 22 = -y + 22 - 22 -11 = -y Now, we divide both sides by -1 to solve for y. -11 / -1 = -y / -1 11 = y So, the other possible value of y is 11.

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Solve for all values of
y in simplest form.

11=|y-22|
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $11=|y-22|$ $\newline$ Answer: $y=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

y

in simplest form.

\newline

11=|y-22|

\newline

Answer:

y=

Given Equation: We are given the equation $11 = |y - 22|$ . The absolute value equation can have two possible cases: either the expression inside the absolute value is positive or it is negative. We will consider both cases to find all possible values of $y$ .
Case $1$ : Case $1$ : The expression inside the absolute value is non-negative, which means $y - 22$ is greater than or equal to $0$ . We can remove the absolute value bars and solve for $y$ . $\newline$ $11 = y - 22$ $\newline$ Now, we add $22$ to both sides of the equation to solve for $y$ . $\newline$ $11 + 22 = y - 22 + 22$ $\newline$ $33 = y$ $\newline$ So, one possible value of $y$ is $33$ .
Case $2$ : Case $2$ : The expression inside the absolute value is negative, which means $y - 22$ is less than $0$ . In this case, we need to consider the opposite of the expression inside the absolute value to be equal to $11$ . $\newline$ $11 = -(y - 22)$ $\newline$ Now, we distribute the negative sign inside the parentheses. $\newline$ $11 = -y + 22$ $\newline$ Next, we subtract $22$ from both sides of the equation to solve for $y$ . $\newline$ $11 - 22 = -y + 22 - 22$ $\newline$ $-11 = -y$ $\newline$ Now, we divide both sides by $-1$ to solve for $y$ . $\newline$ $0$ $1$ $\newline$ $0$ $2$ $\newline$ So, the other possible value of $y$ is $11$ .