Solve for all values of x in simplest form. 1-|x-6|=-3 Answer: x=

Write Equation: Write down the given equation. We have the equation 1 - |x - 6| = -3. Let's isolate the absolute value expression on one side of the equation.Isolate Absolute Value: Add |x - 6| to both sides of the equation to isolate the absolute value expression. 1 - |x - 6| + |x - 6| = -3 + |x - 6| This simplifies to: 1 = -3 + |x - 6|Subtract to Solve: Now, subtract -3 from both sides to solve for |x - 6|. 1 - (-3) = |x - 6| This simplifies to: 4 = |x - 6|Absolute Value Equation: Solve the absolute value equation. The equation |x - 6| = 4 means that the expression inside the absolute value, x - 6, can either be 4 or -4.Set Up Equations: Set up two separate equations to solve for x. x - 6 = 4 or x - 6 = -4Solve First Equation: Solve the first equation x - 6 = 4. Add 6 to both sides of the equation: x - 6 + 6 = 4 + 6 This simplifies to: x = 10Solve Second Equation: Solve the second equation x - 6 = -4. Add 6 to both sides of the equation: x - 6 + 6 = -4 + 6 This simplifies to: x = 2

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Solve for all values of
x in simplest form.

1-|x-6|=-3
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $1-|x-6|=-3$ $\newline$ 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-|x-6|=-3

\newline

Answer:

x=

Write Equation: Write down the given equation. $\newline$ We have the equation $1 - |x - 6| = -3$ . $\newline$ Let's isolate the absolute value expression on one side of the equation.
Isolate Absolute Value: Add |x - 6| ) to both sides of the equation to isolate the absolute value expression.$\newline\$1 - |x - 6| + |x - 6| = -3 + |x - 6|$$\newline$This simplifies to:$\newline$$1 = -3 + |x - 6|$
Subtract to Solve: Now, subtract $-3$ from both sides to solve for $|x - 6|$.$\newline$$1 - (-3) = |x - 6|$$\newline$This simplifies to:$\newline$$4 = |x - 6|$
Absolute Value Equation: Solve the absolute value equation.$\newline$The equation $|x - 6| = 4$ means that the expression inside the absolute value, $x - 6$, can either be $4$ or $-4$.
Set Up Equations: Set up two separate equations to solve for $x$.$x - 6 = 4$ or $x - 6 = -4$
Solve First Equation: Solve the first equation $x - 6 = 4$. Add $6$ to both sides of the equation: $x - 6 + 6 = 4 + 6$ This simplifies to: $x = 10$
Solve Second Equation: Solve the second equation $x - 6 = -4$. Add $6$ to both sides of the equation: $x - 6 + 6 = -4 + 6$ This simplifies to: $x = 2$