Choose all of the correct answers: How many solutions are there to the inequality $$ 3 x+13

Question

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 $$ 3 x+13=-26 $$

UpStudy AI · Accepted Answer

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 $$ 3x +13=-26 $$
The correct answers are "Infinite" and "More than the number of solutions to $$ 3x +13=-26 $$."

Choose all of the correct answers:
How many solutions are there to the inequality ?
No more than 1,000
Infinite
13
26
More than the number of solutions to

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Choose all of the correct answers: How many solutions are there to the inequality ? No more than 1,000 Infinite 13 26 More than the number of solutions to