Choose all of the correct answers: How many solutions are there to the inequality \( 3 x+13<-26 \) ? No more than 1,000 Infinite 13 26 More than the number of solutions to \( 3 x+13=-26 \)

To determine the number of solutions to the inequality \( 3x + 13 < -26 \), let's solve it step by step: 1. **Solve the Inequality:** \[ 3x + 13 < -26 \] Subtract 13 from both sides: \[ 3x < -39 \] Divide by 3: \[ x < -13 \] The inequality \( x < -13 \) has **infinitely many real solutions** since there are no restrictions on how small \( x \) can be, as long as it's less than -13. 2. **Compare with the Equation \( 3x + 13 = -26 \):** Solving the equation: \[ 3x + 13 = -26 \implies 3x = -39 \implies x = -13 \] The equation has exactly **one solution** (\( x = -13 \)). 3. **Assess the Options:** - **No more than 1,000:** This is incorrect because there are infinitely many solutions. - **Infinite:** Correct, as there are infinitely many solutions. - **13:** Incorrect; this refers to a specific number, not the number of solutions. - **26:** Incorrect for the same reason as above. - **More than the number of solutions to \( 3x + 13 = -26 \):** Correct, since the inequality has infinitely many solutions compared to the one solution of the equation. **Correct Answers:** - Infinite - More than the number of solutions to \( 3x +13=-26 \)