Solve for all values of x in simplest form. 4=|2x-11| Answer: x=

Understand absolute value equation: Understand the absolute value equation. The equation 4 = |2x - 11| means that the expression 2x - 11 can be either 4 or -4 because the absolute value of a number is its distance from zero on the number line, which is always non-negative.Set up two equations: Set up two separate equations to solve for x. Since |2x - 11| can be either 4 or -4, we can write two equations: 1. 2x - 11 = 4 2. 2x - 11 = -4Solve first equation: Solve the first equation 2x - 11 = 4. Add 11 to both sides of the equation to isolate the term with x. 2x - 11 + 11 = 4 + 11 2x = 15 Now, divide both sides by 2 to solve for x. x = 15 / 2 x = 7.5Solve second equation: Solve the second equation 2x - 11 = -4. Add 11 to both sides of the equation to isolate the term with x. 2x - 11 + 11 = -4 + 11 2x = 7 Now, divide both sides by 2 to solve for x. x = 7 / 2 x = 3.5

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Solve for all values of
x in simplest form.

4=|2x-11|
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $4=|2 x-11|$ $\newline$ Answer: $x=$

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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

4=|2 x-11|

\newline

Answer:

x=

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $4 = |2x - 11|$ means that the expression $2x - 11$ can be either $4$ or $-4$ because the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Set up two equations: Set up two separate equations to solve for $x$ . Since $|2x - 11|$ can be either $4$ or $-4$ , we can write two equations: $1$ . $2x - 11 = 4$ $2$ . $2x - 11 = -4$
Solve first equation: Solve the first equation $2x - 11 = 4$ . Add $11$ to both sides of the equation to isolate the term with $x$ . $2x - 11 + 11 = 4 + 11$ $2x = 15$ Now, divide both sides by $2$ to solve for $x$ . $x = \frac{15}{2}$ $x = 7.5$
Solve second equation: Solve the second equation $2x - 11 = -4$ . Add $11$ to both sides of the equation to isolate the term with $x$ . $2x - 11 + 11 = -4 + 11$ $2x = 7$ Now, divide both sides by $2$ to solve for $x$ . $x = \frac{7}{2}$ $x = 3.5$