Solve for all values of x in simplest form. 2|x-3|-7=11 Answer: x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. Add 7 to both sides of the equation to get: 2|x - 3| - 7 + 7 = 11 + 7Simplify equation: Simplify both sides of the equation. 2|x - 3| = 18Divide by 2: Divide both sides of the equation by 2 to solve for the absolute value expression. (2|x - 3|) / 2 = 18 / 2Set up two equations: Simplify the equation after dividing. |x - 3| = 9Solve first equation: Set up two separate equations to account for the absolute value, one for the positive value and one for the negative value. x - 3 = 9 or x - 3 = -9Solve second equation: Solve the first equation for x. x - 3 = 9 Add 3 to both sides: x = 9 + 3 x = 12Solve the second equation for x. x - 3 = -9 Add 3 to both sides: x = -9 + 3 x = -6

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Solve for all values of
x in simplest form.

2|x-3|-7=11
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $2|x-3|-7=11$ $\newline$ 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

2|x-3|-7=11

\newline

Answer:

x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. $\newline$ Add $7$ to both sides of the equation to get: $\newline$ $2|x - 3| - 7 + 7 = 11 + 7$
Simplify equation: Simplify both sides of the equation. $2|x - 3| = 18$
Divide by $2$ : Divide both sides of the equation by $2$ to solve for the absolute value expression. $\newline$ $(2|x - 3|) / 2 = 18 / 2$
Set up two equations: Simplify the equation after dividing. $|x - 3| = 9$
Solve first equation: Set up two separate equations to account for the absolute value, one for the positive value and one for the negative value. $\newline$ $x - 3 = 9$ or $x - 3 = -9$
Solve second equation: Solve the first equation for $x$ . $x - 3 = 9$ Add $3$ to both sides: $x = 9 + 3$ $x = 12$
Solve second equation: Solve the first equation for $x$ . $x - 3 = 9$ Add $3$ to both sides: $x = 9 + 3$ $x = 12$ Solve the second equation for $x$ . $x - 3 = -9$ Add $3$ to both sides: $x = -9 + 3$ $x = -6$