Solve for all values of x in simplest form. 54=|6x| Answer: x=

Absolute Value Analysis: We are given the equation 54 = |6x|. The absolute value of a number is always non-negative, and it represents the distance of that number from zero on the number line. Therefore, |6x| can be either 6x or -6x if 6x is negative. We need to consider both cases to find all values of x.Case 1: Non-Negative 6x: First, let's consider the case where 6x is non-negative. We can write the equation without the absolute value as 54 = 6x. To find the value of x, we divide both sides of the equation by 6. x = 54 / 6 x = 9Case 2: Negative 6x: Now, let's consider the case where 6x is negative. In this case, the equation becomes 54 = -6x. Again, we solve for x by dividing both sides of the equation by -6. x = 54 / -6 x = -9

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for all values of
x in simplest form.

54=|6x|
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $54=|6 x|$ $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

54=|6 x|

\newline

Answer:

x=

Absolute Value Analysis: We are given the equation $54 = |6x|$ . The absolute value of a number is always non-negative, and it represents the distance of that number from zero on the number line. Therefore, $|6x|$ can be either $6x$ or $-6x$ if $6x$ is negative. We need to consider both cases to find all values of $x$ .
Case $1$ : Non-Negative $6x$ : First, let's consider the case where $6x$ is non-negative. We can write the equation without the absolute value as $54 = 6x$ . To find the value of $x$ , we divide both sides of the equation by $6$ . $\newline$ $x = \frac{54}{6}$ $\newline$ $x = 9$
Case $2$ : Negative $6x$ : Now, let's consider the case where $6x$ is negative. In this case, the equation becomes $54 = -6x$ . Again, we solve for $x$ by dividing both sides of the equation by $-6$ . $\newline$ $x = \frac{54}{-6}$ $\newline$ $x = -9$