Which of the following is a linear equation? 1) \( \frac{10}{3} x-3=\frac{7}{x}+15 \) 2) \( 3 x^{2}+10 x=5 \) 3) \( \frac{10}{3} x-3=7 x+15 \) 4) \( \sqrt{x}+14=15 x \)

To determine which of the given equations is linear, we need to identify equations where the variable \( x \) appears to the first power and is not involved in any non-linear operations (like being in a denominator or under a square root). Let's examine each equation: 1. **\( \frac{10}{3} x - 3 = \frac{7}{x} + 15 \)** - This equation includes a term with \( \frac{1}{x} \), which makes it nonlinear. 2. **\( 3x^{2} + 10x = 5 \)** - This is a quadratic equation because of the \( x^2 \) term, making it nonlinear. 3. **\( \frac{10}{3} x - 3 = 7x + 15 \)** - Simplifying gives: \[ \frac{10}{3}x - 7x - 18 = 0 \\ \left(\frac{10}{3} - \frac{21}{3}\right)x - 18 = 0 \\ -\frac{11}{3}x - 18 = 0 \] - This equation is linear since \( x \) is to the first power and there's no nonlinear operation on \( x \). 4. **\( \sqrt{x} + 14 = 15x \)** - The presence of \( \sqrt{x} \) (which is \( x^{1/2} \)) makes this equation nonlinear. **Conclusion:** Only the third equation is linear. **Answer:** Only equation 3) \( \frac{10}{3} x-3=7 x+15 \) is a linear equation.