Solve for all values of y in simplest form. 41=|-1+5y| Answer: y=

Write Equation: Write down the given equation and understand that the absolute value expression will yield two possible equations. 41 = |-1 + 5y|Split Cases: Split the absolute value equation into two separate equations, one for the positive case and one for the negative case. The two cases are: 41 = -1 + 5y (when -1 + 5y is positive or zero) 41 = -(-1 + 5y) or 41 = 1 - 5y (when -1 + 5y is negative)Solve Positive Case: Solve the first equation 41 = -1 + 5y. Add 1 to both sides to isolate the term with y. 41 + 1 = -1 + 1 + 5y 42 = 5y Now, divide both sides by 5 to solve for y. 42 / 5 = 5y / 5 y = 42 / 5 y = 8.4Solve Negative Case: Solve the second equation 41 = 1 - 5y. Subtract 1 from both sides to isolate the term with y. 41 - 1 = 1 - 1 - 5y 40 = -5y Now, divide both sides by -5 to solve for y. 40 / -5 = -5y / -5 y = -8

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Solve for all values of
y in simplest form.

41=|-1+5y|
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $41=|-1+5 y|$ $\newline$ 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

41=|-1+5 y|

\newline

Answer:

y=

Write Equation: Write down the given equation and understand that the absolute value expression will yield two possible equations. $\newline$ $41 = |-1 + 5y|$
Split Cases: Split the absolute value equation into two separate equations, one for the positive case and one for the negative case. $\newline$ The two cases are: $\newline$ $41 = -1 + 5y$ (when $-1 + 5y$ is positive or zero) $\newline$ $41 = -(-1 + 5y)$ or $41 = 1 - 5y$ (when $-1 + 5y$ is negative)
Solve Positive Case: Solve the first equation $41 = -1 + 5y$ . Add $1$ to both sides to isolate the term with $y$ . $41 + 1 = -1 + 1 + 5y$ $42 = 5y$ Now, divide both sides by $5$ to solve for $y$ . $42 / 5 = 5y / 5$ $y = 42 / 5$ $y = 8.4$
Solve Negative Case: Solve the second equation $41 = 1 - 5y$ . Subtract $1$ from both sides to isolate the term with $y$ . $41 - 1 = 1 - 1 - 5y$ $40 = -5y$ Now, divide both sides by $-5$ to solve for $y$ . $40 / -5 = -5y / -5$ $y = -8$