Solve for all values of y in simplest form. 14=|y+9| Answer: y=

Understand absolute value equation: Understand the absolute value equation. The equation 14 = |y + 9| means that the expression inside the absolute value, y + 9, is either 14 or -14, because the absolute value of a number is its distance from zero on the number line, which is always non-negative.Set up two equations: Set up two separate equations to solve for y. Since the absolute value of y + 9 can be either positive or negative 14, we write: y + 9 = 14 or y + 9 = -14Solve first equation: Solve the first equation y + 9 = 14. Subtract 9 from both sides to isolate y: y + 9 - 9 = 14 - 9 y = 5Solve second equation: Solve the second equation y + 9 = -14. Subtract 9 from both sides to isolate y: y + 9 - 9 = -14 - 9 y = -23Check solutions: Check the solutions in the original equation. Substitute y = 5 into the original equation: 14 = |5 + 9| 14 = |14| 14 = 14 (True) Now, substitute y = -23 into the original equation: 14 = |-23 + 9| 14 = |-14| 14 = 14 (True) Both solutions check out.

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Solve for all values of
y in simplest form.

14=|y+9|
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $14=|y+9|$ $\newline$ 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

14=|y+9|

\newline

Answer:

y=

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $14 = |y + 9|$ means that the expression inside the absolute value, $y + 9$ , is either $14$ or $-14$ , because the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Set up two equations: Set up two separate equations to solve for $y$ . Since the absolute value of $y + 9$ can be either positive or negative $14$ , we write: $y + 9 = 14$ or $y + 9 = -14$
Solve first equation: Solve the first equation $y + 9 = 14$ . $\newline$ Subtract $9$ from both sides to isolate $y$ : $\newline$ $y + 9 - 9 = 14 - 9$ $\newline$ $y = 5$
Solve second equation: Solve the second equation $y + 9 = -14$ . $\newline$ Subtract $9$ from both sides to isolate $y$ : $\newline$ $y + 9 - 9 = -14 - 9$ $\newline$ $y = -23$
Check solutions: Check the solutions in the original equation. $\newline$ Substitute $y = 5$ into the original equation: $\newline$ $14 = |5 + 9|$ $\newline$ $14 = |14|$ $\newline$ $14 = 14$ (True) $\newline$ Now, substitute $y = -23$ into the original equation: $\newline$ $14 = |-23 + 9|$ $\newline$ $14 = |-14|$ $\newline$ $14 = 14$ (True) $\newline$ Both solutions check out.