Solve for all values of b in simplest form. |(b)/( 12)|=9 Answer: b=

Understand Absolute Value Definition: We are given the absolute value equation |(b)/(12)|=9. To solve for b, we need to consider the definition of absolute value, which states that if |x| = a, then x = a or x = -a for a ≥ 0. Since 9 is positive, we can set up two separate equations: (b)/(12) = 9 and (b)/(12) = -9.Solve for b (Equation 1): Solve the first equation (b)/(12) = 9. To find b, multiply both sides of the equation by 12. b = 9 * 12 b = 108Solve for b (Equation 2): Solve the second equation (b)/(12) = -9. Similarly, multiply both sides of this equation by 12. b = -9 * 12 b = -108Identify Solutions: We have found two solutions for b that satisfy the original equation |(b)/(12)|=9. The solutions are b = 108 and b = -108. These are the values of b in simplest form.

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Solve for all values of
b in simplest form.

|(b)/( 12)|=9
Answer:
b=

Solve for all values of $b$ in simplest form. $\newline$ $\left|\frac{b}{12}\right|=9$ $\newline$ 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

\left|\frac{b}{12}\right|=9

\newline

Answer:

b=

Understand Absolute Value Definition: We are given the absolute value equation $|\frac{b}{12}|=9$ . To solve for $b$ , we need to consider the definition of absolute value, which states that if $|x| = a$ , then $x = a$ or $x = -a$ for $a \geq 0$ . Since $9$ is positive, we can set up two separate equations: $\frac{b}{12} = 9$ and $\frac{b}{12} = -9$ .
Solve for b (Equation $1$ ): Solve the first equation $\frac{b}{12} = 9$ . To find b, multiply both sides of the equation by $12$ . $\newline$ $b = 9 \times 12$ $\newline$ $b = 108$
Solve for $b$ (Equation $2$ ): Solve the second equation $\frac{b}{12} = -9$ . Similarly, multiply both sides of this equation by $12$ . $\newline$ $b = -9 \times 12$ $\newline$ $b = -108$
Identify Solutions: We have found two solutions for $b$ that satisfy the original equation $\left|\frac{b}{12}\right|=9$ . The solutions are $b = 108$ and $b = -108$ . These are the values of $b$ in simplest form.