Solve for all values of y in simplest form. 18=|-3y+10| Answer: y=

Understand absolute value equation: Understand the absolute value equation. The equation 18 = |-3y + 10| means that the expression inside the absolute value, -3y + 10, can be either positive or negative, but its absolute value must be 18.Set up two equations: Set up two separate equations to remove the absolute value. Since the absolute value of a number can be either positive or negative, we have two cases: Case 1: -3y + 10 = 18 Case 2: -3y + 10 = -18Solve first case: Solve the first case. Starting with Case 1: -3y + 10 = 18 Subtract 10 from both sides to isolate the term with y. -3y + 10 - 10 = 18 - 10 -3y = 8 Now, divide both sides by -3 to solve for y. y = 8 / -3 y = -8/3Solve second case: Solve the second case. Now for Case 2: -3y + 10 = -18 Subtract 10 from both sides to isolate the term with y. -3y + 10 - 10 = -18 - 10 -3y = -28 Divide both sides by -3 to solve for y. y = -28 / -3 y = 28/3

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Solve for all values of
y in simplest form.

18=|-3y+10|
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $18=|-3 y+10|$ $\newline$ Answer: $y=$

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Precalculus

Solve logarithmic equations with multiple logarithms

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Q. Solve for all values of

y

in simplest form.

\newline

18=|-3 y+10|

\newline

Answer:

y=

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $18 = |-3y + 10|$ means that the expression inside the absolute value, $-3y + 10$ , can be either positive or negative, but its absolute value must be $18$ .
Set up two equations: Set up two separate equations to remove the absolute value. $\newline$ Since the absolute value of a number can be either positive or negative, we have two cases: $\newline$ Case $1$ : $-3y + 10 = 18$ $\newline$ Case $2$ : $-3y + 10 = -18$
Solve first case: Solve the first case. $\newline$ Starting with Case $1$ : $-3y + 10 = 18$ $\newline$ Subtract $10$ from both sides to isolate the term with $y$ . $\newline$ $-3y + 10 - 10 = 18 - 10$ $\newline$ $-3y = 8$ $\newline$ Now, divide both sides by $-3$ to solve for $y$ . $\newline$ $y = \frac{8}{-3}$ $\newline$ $y = -\frac{8}{3}$
Solve second case: Solve the second case. $\newline$ Now for Case $2$ : $-3y + 10 = -18$ $\newline$ Subtract $10$ from both sides to isolate the term with $y$ . $\newline$ $-3y + 10 - 10 = -18 - 10$ $\newline$ $-3y = -28$ $\newline$ Divide both sides by $-3$ to solve for $y$ . $\newline$ $y = -28 / -3$ $\newline$ $y = 28/3$