Solve for all values of y in simplest form. |4-3y|=19 Answer: y=

Absolute Value Equation Explanation: We are given the absolute value equation |4-3y|=19. 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 expression inside the absolute value can be either positive or equal to 19, or negative and its absolute value equal to 19. We can set up two separate equations to solve for y: 4 - 3y = 19 or 4 - 3y = -19First Equation Solution: Let's solve the first equation 4 - 3y = 19. Subtract 4 from both sides to isolate the term with y. 4 - 3y - 4 = 19 - 4 -3y = 15 Now, divide both sides by -3 to solve for y. y = 15 / -3 y = -5Second Equation Solution: Now let's solve the second equation 4 - 3y = -19. Subtract 4 from both sides to isolate the term with y. 4 - 3y - 4 = -19 - 4 -3y = -23 Now, divide both sides by -3 to solve for y. y = -23 / -3 y = 23 / 3 y = 7.666... or y = 7\frac{2}{3}

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Solve for all values of
y in simplest form.

|4-3y|=19
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $|4-3 y|=19$ $\newline$ 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

|4-3 y|=19

\newline

Answer:

y=

Absolute Value Equation Explanation: We are given the absolute value equation $|4-3y|=19$ . 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 expression inside the absolute value can be either positive or equal to $19$ , or negative and its absolute value equal to $19$ . We can set up two separate equations to solve for $y$ : $4 - 3y = 19$ or $4 - 3y = -19$
First Equation Solution: Let's solve the first equation $4 - 3y = 19$ . Subtract $4$ from both sides to isolate the term with $y$ . $4 - 3y - 4 = 19 - 4$ $-3y = 15$ Now, divide both sides by $-3$ to solve for $y$ . $y = 15 / -3$ $y = -5$
Second Equation Solution: Now let's solve the second equation $4 - 3y = -19$ . $\newline$ Subtract $4$ from both sides to isolate the term with $y$ . $\newline$ $4 - 3y - 4 = -19 - 4$ $\newline$ $-3y = -23$ $\newline$ Now, divide both sides by $-3$ to solve for $y$ . $\newline$ $y = -23 / -3$ $\newline$ $y = 23 / 3$ $\newline$ $y = 7.666...$ or $4$ $0$