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Solve the equation:

[tex]\[ |2x + 7| - 3 = 11 \][/tex]

Enter the exact answers.

The field below accepts a list of numbers or formulas separated by semicolons (e.g., [tex]\(2; 4; 6\)[/tex] or [tex]\(x + 1; x - 1\)[/tex]). The order of the list does not matter.

[tex]\[ x = \][/tex]



Answer :

GinnyAnswer
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]

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