Solve for all values of x in simplest form. 6-4|9+2x|=-42 Answer: x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. We have the equation 6 - 4|9 + 2x| = -42. Subtract 6 from both sides to get -4|9 + 2x| = -48.Divide by -4: Divide both sides by -4 to solve for the absolute value expression. -4|9 + 2x| = -48 becomes |9 + 2x| = 12 after dividing both sides by -4.Set up two equations: Set up two separate equations to account for the definition of absolute value. Since |9 + 2x| = 12, we have two possibilities: 1. 9 + 2x = 12 2. 9 + 2x = -12Solve first equation: Solve the first equation 9 + 2x = 12. Subtract 9 from both sides to isolate the term with x. 2x = 12 - 9 2x = 3 Now, divide by 2 to solve for x. x = 3 / 2 x = 1.5Solve second equation: Solve the second equation 9 + 2x = -12. Subtract 9 from both sides to isolate the term with x. 2x = -12 - 9 2x = -21 Now, divide by 2 to solve for x. x = -21 / 2 x = -10.5

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Solve for all values of
x in simplest form.

6-4|9+2x|=-42
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $6-4|9+2 x|=-42$ $\newline$ 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

6-4|9+2 x|=-42

\newline

Answer:

x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. $\newline$ We have the equation $6 - 4|9 + 2x| = -42$ . $\newline$ Subtract $6$ from both sides to get $-4|9 + 2x| = -48$ .
Divide by $-4$ : Divide both sides by $-4$ to solve for the absolute value expression. $-4|9 + 2x| = -48$ becomes $|9 + 2x| = 12$ after dividing both sides by $-4$ .
Set up two equations: Set up two separate equations to account for the definition of absolute value. $\newline$ Since $|9 + 2x| = 12$ , we have two possibilities: $\newline$ $1$ . $9 + 2x = 12$ $\newline$ $2$ . $9 + 2x = -12$
Solve first equation: Solve the first equation $9 + 2x = 12$ . Subtract $9$ from both sides to isolate the term with $x$ . $2x = 12 - 9$ $2x = 3$ Now, divide by $2$ to solve for $x$ . $x = \frac{3}{2}$ $x = 1.5$
Solve second equation: Solve the second equation $9 + 2x = -12$ . Subtract $9$ from both sides to isolate the term with $x$ . $2x = -12 - 9$ $2x = -21$ Now, divide by $2$ to solve for $x$ . $x = -21 / 2$ $x = -10.5$