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Solve for all values of x in simplest form. 64=|8x| Answer: x=

Solve for all values of x x in simplest form.\newline64=∣8x∣ 64=|8 x| \newlineAnswer: x= x=

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Evaluate absolute value expressionsright chevron icon

Full solution

Q. Solve for all values of x x in simplest form.\newline64=∣8x∣ 64=|8 x| \newlineAnswer: x= x=
  1. Understand absolute value equation: Understand the absolute value equation.\newlineThe absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, ∣8x∣|8x| can be either 8x8x or −8x-8x, depending on the value of xx.
  2. Set up two equations: Set up two separate equations to solve for xx. Since ∣8x∣|8x| can be either 8x8x or −8x-8x, we have two cases to consider: Case 11: 8x=648x = 64 Case 22: −8x=64-8x = 64
  3. Solve for x in Case 11: Solve for x in Case 11.\newlineDivide both sides of the equation by 88 to isolate x:\newline8x=648x = 64\newlinex=648x = \frac{64}{8}\newlinex=8x = 8
  4. Solve for x in Case 22: Solve for x in Case 22.\newlineDivide both sides of the equation by −8-8 to isolate xx:\newline−8x=64-8x = 64\newlinex=64−8x = \frac{64}{-8}\newlinex=−8x = -8

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