Question

solve for x ecuation samples

Answer 1

Sure! Here are some examples of equations along with their solutions for \( x \):

### 1. Linear Equation
**Equation:** \( 2x + 3 = 11 \)

**Solution:**
\[
2x + 3 - 3 = 11 - 3 \\
2x = 8 \\
x = \frac{8}{2} \\
x = 4
\]

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### 2. Quadratic Equation
**Equation:** \( x^2 - 5x + 6 = 0 \)

**Solution:**
Factoring the quadratic,
\[
(x - 2)(x - 3) = 0
\]
Setting each factor to zero:
\[
x - 2 = 0 \quad \Rightarrow \quad x = 2 \\
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]
So, \( x = 2 \) or \( x = 3 \).

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### 3. Absolute Value Equation
**Equation:** \( |2x - 4| = 6 \)

**Solution:**
This gives two cases:
1. \( 2x - 4 = 6 \)
\[
2x = 10 \\
x = 5
\]
2. \( 2x - 4 = -6 \)
\[
2x = -2 \\
x = -1
\]
So, \( x = 5 \) or \( x = -1 \).

---

### 4. Exponential Equation
**Equation:** \( 3^x = 81 \)

**Solution:**
Rewrite \( 81 \) as \( 3^4 \):
\[
3^x = 3^4 \\
x = 4
\]

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### 5. Logarithmic Equation
**Equation:** \( \log_2(x) = 3 \)

**Solution:**
Convert to exponential form:
\[
x = 2^3 \\
x = 8
\]

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If you'd like to see more specific types of equations or need help with a particular one, just let me know!