Solve for all values of x in simplest form. 12=|5x-15| Answer: x=

Given Equation: We are given the equation 12 = |5x - 15|. The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.Positive Case: First, let's consider the positive case where the expression inside the absolute value is non-negative. We set 5x - 15 equal to 12 and solve for x. 5x - 15 = 12Positive Case Solution: Add 15 to both sides of the equation to isolate the term with x. 5x - 15 + 15 = 12 + 15 5x = 27Negative Case: Divide both sides by 5 to solve for x. 5x / 5 = 27 / 5 x = 27 / 5 x = 5.4Negative Case Solution: Now, let's consider the negative case where the expression inside the absolute value is negative. We set 5x - 15 equal to -12 and solve for x. 5x - 15 = -12Add 15 to both sides of the equation to isolate the term with x. 5x - 15 + 15 = -12 + 15 5x = 3Divide both sides by 5 to solve for x. 5x / 5 = 3 / 5 x = 3 / 5 x = 0.6

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

12=|5 x-15|

\newline

Answer:

x=

Given Equation: We are given the equation $12 = |5x - 15|$ . The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.
Positive Case: First, let's consider the positive case where the expression inside the absolute value is non-negative. We set $5x - 15$ equal to $12$ and solve for $x$ . $5x - 15 = 12$
Positive Case Solution: Add $15$ to both sides of the equation to isolate the term with $x$ . $\newline$ $5x - 15 + 15 = 12 + 15$ $\newline$ $5x = 27$
Negative Case: Divide both sides by $5$ to solve for $x$ . $\frac{5x}{5} = \frac{27}{5}$ $x = \frac{27}{5}$ $x = 5.4$
Negative Case Solution: Now, let's consider the negative case where the expression inside the absolute value is negative. We set $5x - 15$ equal to $-12$ and solve for $x$ . $5x - 15 = -12$
Negative Case Solution: Now, let's consider the negative case where the expression inside the absolute value is negative. We set $5x - 15$ equal to $-12$ and solve for $x$ . $\newline$ $5x - 15 = -12$ Add $15$ to both sides of the equation to isolate the term with $x$ . $\newline$ $5x - 15 + 15 = -12 + 15$ $\newline$ $5x = 3$
Negative Case Solution: Now, let's consider the negative case where the expression inside the absolute value is negative. We set $5x - 15$ equal to $-12$ and solve for $x$ . $\newline$ $5x - 15 = -12$ Add $15$ to both sides of the equation to isolate the term with $x$ . $\newline$ $5x - 15 + 15 = -12 + 15$ $\newline$ $5x = 3$ Divide both sides by $5$ to solve for $x$ . $\newline$ $-12$ $0$ $\newline$ $-12$ $1$ $\newline$ $x = $0$.$6$