Answer :
To solve the equation [tex]\(2|x-5|-1=5\)[/tex], we can follow these steps:
1. Isolate the absolute value expression:
Start by adding 1 to both sides of the equation:
[tex]\[
2|x-5|-1 + 1 = 5 + 1
\][/tex]
which simplifies to:
[tex]\[
2|x-5| = 6
\][/tex]
2. Solve for the absolute value:
Next, divide both sides by 2 to isolate the absolute value:
[tex]\[
|x-5| = \frac{6}{2}
\][/tex]
which simplifies to:
[tex]\[
|x-5| = 3
\][/tex]
3. Break down the absolute value into two cases:
The equation [tex]\(|x-5| = 3\)[/tex] means there are two possible cases:
- Case 1: [tex]\(x-5 = 3\)[/tex]
- Case 2: [tex]\(x-5 = -3\)[/tex]
4. Solve each case separately:
- For Case 1: [tex]\(x-5 = 3\)[/tex],
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For Case 2: [tex]\(x-5 = -3\)[/tex],
[tex]\[
x = -3 + 5 = 2
\][/tex]
5. State the solutions:
Therefore, the solutions to the equation [tex]\(2|x-5|-1=5\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].
The correct options for the solutions are [tex]\(x = 2\)[/tex] or [tex]\(x = 8\)[/tex].
1. Isolate the absolute value expression:
Start by adding 1 to both sides of the equation:
[tex]\[
2|x-5|-1 + 1 = 5 + 1
\][/tex]
which simplifies to:
[tex]\[
2|x-5| = 6
\][/tex]
2. Solve for the absolute value:
Next, divide both sides by 2 to isolate the absolute value:
[tex]\[
|x-5| = \frac{6}{2}
\][/tex]
which simplifies to:
[tex]\[
|x-5| = 3
\][/tex]
3. Break down the absolute value into two cases:
The equation [tex]\(|x-5| = 3\)[/tex] means there are two possible cases:
- Case 1: [tex]\(x-5 = 3\)[/tex]
- Case 2: [tex]\(x-5 = -3\)[/tex]
4. Solve each case separately:
- For Case 1: [tex]\(x-5 = 3\)[/tex],
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For Case 2: [tex]\(x-5 = -3\)[/tex],
[tex]\[
x = -3 + 5 = 2
\][/tex]
5. State the solutions:
Therefore, the solutions to the equation [tex]\(2|x-5|-1=5\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].
The correct options for the solutions are [tex]\(x = 2\)[/tex] or [tex]\(x = 8\)[/tex].