Solve for all values of a in simplest form. 3=|(a)/(6)| Answer: a=

Equation Definition: We have the equation 3 = |a/6|. To find the values of a, we need to consider the definition of absolute value. The absolute value of a number is the distance of that number from zero on the number line, which is always non-negative. Therefore, |a/6| can be 3 or -3 because both would result in a positive 3 after taking the absolute value.Positive Case: Let's first consider when a/6 is positive. We set a/6 equal to 3 and solve for a. a/6 = 3 Multiply both sides by 6 to isolate a. a = 3 * 6 a = 18Negative Case: Now let's consider when a/6 is negative. We set a/6 equal to -3 and solve for a. a/6 = -3 Multiply both sides by 6 to isolate a. a = -3 * 6 a = -18

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Solve for all values of
a in simplest form.

3=|(a)/(6)|
Answer:
a=

Solve for all values of $a$ in simplest form. $\newline$ $3=\left|\frac{a}{6}\right|$ $\newline$ Answer: $a=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

a

in simplest form.

\newline

3=\left|\frac{a}{6}\right|

\newline

Answer:

a=

Equation Definition: We have the equation $3 = |\frac{a}{6}|$ . To find the values of $a$ , we need to consider the definition of absolute value. The absolute value of a number is the distance of that number from zero on the number line, which is always non-negative. Therefore, $|\frac{a}{6}|$ can be $3$ or $-3$ because both would result in a positive $3$ after taking the absolute value.
Positive Case: Let's first consider when $a/6$ is positive. We set $a/6$ equal to $3$ and solve for $a$ . $\newline$ $a/6 = 3$ $\newline$ Multiply both sides by $6$ to isolate $a$ . $\newline$ $a = 3 \times 6$ $\newline$ $a = 18$
Negative Case: Now let's consider when $a/6$ is negative. We set $a/6$ equal to $-3$ and solve for $a$ . $\newline$ $a/6 = -3$ $\newline$ Multiply both sides by $6$ to isolate $a$ . $\newline$ $a = -3 \times 6$ $\newline$ $a = -18$