Solve for all values of y in simplest form. |-15+2y|=6 Answer: y=

Given Equation: We are given the absolute value equation |-15 + 2y| = 6. 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 either be positive or negative, but the absolute value itself is positive or zero. To solve the equation, we need to consider both cases where -15 + 2y is positive and where it is negative.Case 1: Positive or Zero: First, let's consider the case where the expression inside the absolute value is positive or zero, which means -15 + 2y itself is equal to 6. So we set up the equation -15 + 2y = 6. Now, we solve for y by adding 15 to both sides of the equation. -15 + 2y + 15 = 6 + 15 2y = 21 Next, we divide both sides by 2 to isolate y. 2y / 2 = 21 / 2 y = 10.5Case 2: Negative: Next, let's consider the case where the expression inside the absolute value is negative, which means -15 + 2y is equal to -6. So we set up the equation -15 + 2y = -6. We solve for y by adding 15 to both sides of the equation. -15 + 2y + 15 = -6 + 15 2y = 9 Now, we divide both sides by 2 to isolate y. 2y / 2 = 9 / 2 y = 4.5

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Solve for all values of
y in simplest form.

|-15+2y|=6
Answer:
y=

Solve for all values of $y$ in simplest form. $\newline$ $|-15+2 y|=6$ $\newline$ 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

|-15+2 y|=6

\newline

Answer:

y=

Given Equation: We are given the absolute value equation $|-15 + 2y| = 6$ . 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 either be positive or negative, but the absolute value itself is positive or zero. To solve the equation, we need to consider both cases where $-15 + 2y$ is positive and where it is negative.
Case $1$ : Positive or Zero: First, let's consider the case where the expression inside the absolute value is positive or zero, which means $-15 + 2y$ itself is equal to $6$ . So we set up the equation $-15 + 2y = 6$ . Now, we solve for $y$ by adding $15$ to both sides of the equation. $-15 + 2y + 15 = 6 + 15$ $2y = 21$ Next, we divide both sides by $2$ to isolate $y$ . $\frac{2y}{2} = \frac{21}{2}$ $6$ $0$
Case $2$ : Negative: Next, let's consider the case where the expression inside the absolute value is negative, which means $-15 + 2y$ is equal to $-6$ . So we set up the equation $-15 + 2y = -6$ . We solve for $y$ by adding $15$ to both sides of the equation. $-15 + 2y + 15 = -6 + 15$ $2y = 9$ Now, we divide both sides by $2$ to isolate $y$ . $\frac{2y}{2} = \frac{9}{2}$ $-6$ $0$