Here's a detailed, step-by-step solution to solving the equation [tex]\(|2x + 7| - 3 = 11\)[/tex].
1. Isolate the absolute value expression:
Add 3 to both sides to get rid of the [tex]\(-3\)[/tex]:
[tex]\[
|2x + 7| = 14
\][/tex]
2. Set up two cases for the absolute value equation:
The absolute value equation [tex]\(|2x + 7| = 14\)[/tex] can be broken into two separate cases:
- Case 1: [tex]\(2x + 7 = 14\)[/tex]
- Case 2: [tex]\(2x + 7 = -14\)[/tex]
3. Solve Case 1: [tex]\(2x + 7 = 14\)[/tex]
- Subtract 7 from both sides:
[tex]\[
2x = 14 - 7
\][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{7}{2}
\][/tex]
[tex]\[
x = 3.5
\][/tex]
4. Solve Case 2: [tex]\(2x + 7 = -14\)[/tex]
- Subtract 7 from both sides:
[tex]\[
2x = -14 - 7
\][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-21}{2}
\][/tex]
[tex]\[
x = -10.5
\][/tex]
So, the solutions to the equation [tex]\(|2x + 7| - 3 = 11\)[/tex] are:
[tex]\[
x = 3.5 \quad \text{and} \quad x = -10.5
\][/tex]
When formatted appropriately for the field that accepts a list of numbers, you enter:
[tex]\[
x = 3.5; -10.5
\][/tex]
