Solve for all values of x in simplest form. 6-2|7+2x|=2 Answer: x=

Isolate absolute value: Isolate the absolute value expression. We start by isolating the absolute value on one side of the equation. 6 - 2|7 + 2x| = 2 Subtract 6 from both sides to get: -2|7 + 2x| = 2 - 6 -2|7 + 2x| = -4Divide by -2: Divide both sides by -2 to solve for the absolute value expression. -2|7 + 2x| = -4 Divide both sides by -2 to get: |7 + 2x| = 2Set up equations: Set up two equations to remove the absolute value, since |A| = B implies A = B or A = -B. 7 + 2x = 2 or 7 + 2x = -2Solve first equation: Solve the first equation 7 + 2x = 2. Subtract 7 from both sides: 2x = 2 - 7 2x = -5 Divide both sides by 2: x = -5/2Solve second equation: Solve the second equation 7 + 2x = -2. Subtract 7 from both sides: 2x = -2 - 7 2x = -9 Divide both sides by 2: x = -9/2

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Solve for all values of
x in simplest form.

6-2|7+2x|=2
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $6-2|7+2 x|=2$ $\newline$ 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

6-2|7+2 x|=2

\newline

Answer:

x=

Isolate absolute value: Isolate the absolute value expression. $\newline$ We start by isolating the absolute value on one side of the equation. $\newline$ $6 - 2|7 + 2x| = 2$ $\newline$ Subtract $6$ from both sides to get: $\newline$ $-2|7 + 2x| = 2 - 6$ $\newline$ $-2|7 + 2x| = -4$
Divide by $-2$ : Divide both sides by $-2$ to solve for the absolute value expression. $-2|7 + 2x| = -4$ Divide both sides by $-2$ to get: $|7 + 2x| = 2$
Set up equations: Set up two equations to remove the absolute value, since $|A| = B$ implies $A = B$ or $A = -B$ . $7 + 2x = 2$ or $7 + 2x = -2$
Solve first equation: Solve the first equation $7 + 2x = 2$ . $\newline$ Subtract $7$ from both sides: $\newline$ $2x = 2 - 7$ $\newline$ $2x = -5$ $\newline$ Divide both sides by $2$ : $\newline$ $x = -\frac{5}{2}$
Solve second equation: Solve the second equation $7 + 2x = -2$ . $\newline$ Subtract $7$ from both sides: $\newline$ $2x = -2 - 7$ $\newline$ $2x = -9$ $\newline$ Divide both sides by $2$ : $\newline$ $x = -\frac{9}{2}$