Solve for all values of b in simplest form. |14-2b|=3 Answer: b=

Absolute Value Case 1: We have the absolute value equation |14 - 2b| = 3. To solve for b, we need to consider the two cases that arise from the definition of absolute value. The expression inside the absolute value can be either positive or equal to 3, or negative and its absolute value equal to 3.Positive Expression Solution: First, let's consider the case where the expression inside the absolute value is positive or zero and equal to 3. This gives us the equation: 14 - 2b = 3 Now, we solve for b by subtracting 14 from both sides of the equation. -2b = 3 - 14 -2b = -11 Next, we divide both sides by -2 to isolate b. b = -11 / -2 b = 11/2Absolute Value Case 2: Now, let's consider the case where the expression inside the absolute value is negative and its absolute value is equal to 3. This gives us the equation: 14 - 2b = -3 We solve for b by subtracting 14 from both sides of the equation. -2b = -3 - 14 -2b = -17 Next, we divide both sides by -2 to isolate b. b = -17 / -2 b = 17/2

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Solve for all values of
b in simplest form.

|14-2b|=3
Answer:
b=

Solve for all values of $b$ in simplest form. $\newline$ $|14-2 b|=3$ $\newline$ Answer: $b=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

b

in simplest form.

\newline

|14-2 b|=3

\newline

Answer:

b=

Absolute Value Case $1$ : We have the absolute value equation $|14 - 2b| = 3$ . To solve for $b$ , we need to consider the two cases that arise from the definition of absolute value. The expression inside the absolute value can be either positive or equal to $3$ , or negative and its absolute value equal to $3$ .
Positive Expression Solution: First, let's consider the case where the expression inside the absolute value is positive or zero and equal to $3$ . This gives us the equation: $\newline$ $14 - 2b = 3$ $\newline$ Now, we solve for $b$ by subtracting $14$ from both sides of the equation. $\newline$ $-2b = 3 - 14$ $\newline$ $-2b = -11$ $\newline$ Next, we divide both sides by $-2$ to isolate $b$ . $\newline$ $b = -11 / -2$ $\newline$ $b = 11/2$
Absolute Value Case $2$ : Now, let's consider the case where the expression inside the absolute value is negative and its absolute value is equal to $3$ . This gives us the equation: $\newline$ $14 - 2b = -3$ $\newline$ We solve for $b$ by subtracting $14$ from both sides of the equation. $\newline$ $-2b = -3 - 14$ $\newline$ $-2b = -17$ $\newline$ Next, we divide both sides by $-2$ to isolate $b$ . $\newline$ $b = -17 / -2$ $\newline$ $b = 17/2$