Solve for all values of x in simplest form. |3x+8|=11 Answer: x=

Absolute Value Equation: We have the absolute value equation |3x + 8| = 11. The absolute value of a number is the distance of that number from zero on the number line, which means it is always non-negative. Therefore, 3x + 8 can either be 11 or -11.Case 1: Positive or Zero: First, let's consider the case when 3x + 8 is positive or zero, which gives us 3x + 8 = 11. Subtract 8 from both sides to isolate the term with x. 3x + 8 - 8 = 11 - 8 3x = 3Case 2: Negative: Now, divide both sides by 3 to solve for x. 3x / 3 = 3 / 3 x = 1 This is our first solution.First Solution: Next, let's consider the case when 3x + 8 is negative, which gives us 3x + 8 = -11. Subtract 8 from both sides to isolate the term with x. 3x + 8 - 8 = -11 - 8 3x = -19Second Solution: Now, divide both sides by 3 to solve for x. 3x / 3 = -19 / 3 x = -19/3 This is our second solution.

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.

|3x+8|=11
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $|3 x+8|=11$ $\newline$ 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

|3 x+8|=11

\newline

Answer:

x=

Absolute Value Equation: We have the absolute value equation $|3x + 8| = 11$ . The absolute value of a number is the distance of that number from zero on the number line, which means it is always non-negative. Therefore, $3x + 8$ can either be $11$ or $-11$ .
Case $1$ : Positive or Zero: First, let's consider the case when $3x + 8$ is positive or zero, which gives us $3x + 8 = 11$ . $\newline$ Subtract $8$ from both sides to isolate the term with $x$ . $\newline$ $3x + 8 - 8 = 11 - 8$ $\newline$ $3x = 3$
Case $2$ : Negative: Now, divide both sides by $3$ to solve for $x$ . $\frac{3x}{3} = \frac{3}{3}$ $x = 1$ This is our first solution.
First Solution: Next, let's consider the case when $3x + 8$ is negative, which gives us $3x + 8 = -11$ . $\newline$ Subtract $8$ from both sides to isolate the term with $x$ . $\newline$ $3x + 8 - 8 = -11 - 8$ $\newline$ $3x = -19$
Second Solution: Now, divide both sides by $3$ to solve for $x$ . $\frac{3x}{3} = \frac{-19}{3}$ $x = \frac{-19}{3}$ This is our second solution.