Solve for all values of b in simplest form. |5b+8|=16 Answer: b=

Absolute Value Equation: We have the absolute value equation |5b + 8| = 16. 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, 5b + 8 can either be 16 or -16.Case 1: Positive or Zero: First, let's consider the case when 5b + 8 is positive or zero, which gives us 5b + 8 = 16. Subtract 8 from both sides to isolate the term with b. 5b + 8 - 8 = 16 - 8 5b = 8Case 1: Negative: Now, divide both sides by 5 to solve for b. 5b / 5 = 8 / 5 b = 8 / 5 b = 1.6Solving for b (Positive): Next, let's consider the case when 5b + 8 is negative, which gives us 5b + 8 = -16. Subtract 8 from both sides to isolate the term with b. 5b + 8 - 8 = -16 - 8 5b = -24Solving for b (Negative): Now, divide both sides by 5 to solve for b. 5b / 5 = -24 / 5 b = -24 / 5 b = -4.8

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Solve for all values of
b in simplest form.

|5b+8|=16
Answer:
b=

Solve for all values of $b$ in simplest form. $\newline$ $|5 b+8|=16$ $\newline$ 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

|5 b+8|=16

\newline

Answer:

b=

Absolute Value Equation: We have the absolute value equation $|5b + 8| = 16$ . 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, $5b + 8$ can either be $16$ or $-16$ .
Case $1$ : Positive or Zero: First, let's consider the case when $5b + 8$ is positive or zero, which gives us $5b + 8 = 16$ . $\newline$ Subtract $8$ from both sides to isolate the term with $b$ . $\newline$ $5b + 8 - 8 = 16 - 8$ $\newline$ $5b = 8$
Case $1$ : Negative: Now, divide both sides by $5$ to solve for $b$ . $\newline$ $\frac{5b}{5} = \frac{8}{5}$ $\newline$ $b = \frac{8}{5}$ $\newline$ $b = 1.6$
Solving for b (Positive): Next, let's consider the case when $5b + 8$ is negative, which gives us $5b + 8 = -16$ .
Subtract $8$ from both sides to isolate the term with $b$ .
$5b + 8 - 8 = -16 - 8$
$5b = -24$
Solving for b (Negative): Now, divide both sides by $5$ to solve for b. $\newline$ $\frac{5b}{5} = \frac{-24}{5}$ $\newline$ $b = \frac{-24}{5}$ $\newline$ $b = -4.8$