Solve for all values of x in simplest form. 1+4|10+2x|=45 Answer: x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. Subtract 1 from both sides of the equation to get: 1 + 4|10 + 2x| - 1 = 45 - 1 4|10 + 2x| = 44Divide by 4: Divide both sides of the equation by 4 to solve for the absolute value expression. 4|10 + 2x| / 4 = 44 / 4 |10 + 2x| = 11Set up two equations: Set up two separate equations to account for the two possible cases of the absolute value (one where the expression inside is positive and one where it is negative). Case 1: 10 + 2x = 11 Case 2: 10 + 2x = -11Solve for x in Case 1: Solve for x in Case 1. 10 + 2x = 11 Subtract 10 from both sides: 2x = 11 - 10 2x = 1 Divide by 2: x = 1 / 2Solve for x in Case 2: Solve for x in Case 2. 10 + 2x = -11 Subtract 10 from both sides: 2x = -11 - 10 2x = -21 Divide by 2: x = -21 / 2

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Solve for all values of
x in simplest form.

1+4|10+2x|=45
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $1+4|10+2 x|=45$ $\newline$ 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

1+4|10+2 x|=45

\newline

Answer:

x=

Isolate absolute value expression: Start by isolating the absolute value expression on one side of the equation. $\newline$ Subtract $1$ from both sides of the equation to get: $\newline$ $1 + 4|10 + 2x| - 1 = 45 - 1$ $\newline$ $4|10 + 2x| = 44$
Divide by $4$ : Divide both sides of the equation by $4$ to solve for the absolute value expression. $\newline$ $\frac{4|10 + 2x|}{4} = \frac{44}{4}$ $\newline$ $|10 + 2x| = 11$
Set up two equations: Set up two separate equations to account for the two possible cases of the absolute value (one where the expression inside is positive and one where it is negative). $\newline$ Case $1$ : $10 + 2x = 11$ $\newline$ Case $2$ : $10 + 2x = -11$
Solve for x in Case $1$ : Solve for x in Case $1$ . $\newline$ $10 + 2x = 11$ $\newline$ Subtract $10$ from both sides: $\newline$ $2x = 11 - 10$ $\newline$ $2x = 1$ $\newline$ Divide by $2$ : $\newline$ $x = \frac{1}{2}$
Solve for x in Case $2$ : Solve for x in Case $2$ . $\newline$ $10 + 2x = -11$ $\newline$ Subtract $10$ from both sides: $\newline$ $2x = -11 - 10$ $\newline$ $2x = -21$ $\newline$ Divide by $2$ : $\newline$ $x = -21 / 2$