11. After combining like terms to simplify the equation 3−15x+24+16x=4x−24−4x , what would be the next best step to finish solving?(1 point) Responses Divide both sides of the equation by 15. Divide both sides of the equation by 15. Subtract 27 from both sides of the equation. Subtract 27 from both sides of the equation. Add x to both sides of the equation. Add x to both sides of the equation. Subtract x from both sides of the equation. Subtract x from both sides of the equation. Subtract 24 from both sides of the equation.

Question

GPT-4o mini · Answer

Let's first simplify the equation $3 - 15x + 24 + 16x = 4x - 24 - 4x$. Combining like terms on the left side: - Combine constants: $3 + 24 = 27$ - Combine $x$ terms: $-15x + 16x = x$ So the left side simplifies to: $$27 + x$$ Now simplify the right side: - Combine like terms: $4x - 4x = 0$ and therefore the right side simplifies to $-24$. So now we have: $$27 + x = -24$$ The next best step to isolate $x$ would be to subtract 27 from both sides of the equation. So, the correct response is: **Subtract 27 from both sides of the equation.**

Answer

12. Which inequality represents the graph below: (1 point) Responses −3x−7≥−10 negative 3 x minus 7 is greater than or equal to negative 10 3x+7>10 3 x plus 7 is greater than 10 3x−7≤−10 3 x minus 7 is less than or equal to negative 10 −3x+7<10 the numberline shows one filled and the line going to the left to -10

GPT-4o mini · Answer

Based on your description, it appears that the number line shows a point filled at -10 and the line extending to the left. This typically indicates that all values less than or equal to -10 are included in the solution.

Now let's analyze the response options:

$-3x - 7 \geq -10$: This means that the expression $-3x - 7$ is greater than or equal to $-10$.
$3x + 7 > 10$: This means $3x + 7$ is greater than 10.
$3x - 7 \leq -10$: This means $3x - 7$ is less than or equal to -10.
$-3x + 7 < 10$: This means $-3x + 7$ is less than 10.

The key to finding the correct inequality is understanding that because the filled point includes -10, it signifies "less than or equal to" for the direction going left on the number line.

Of the options given, $3x - 7 \leq -10$ correctly conveys this condition, indicating that $3x - 7$ is less than or equal to -10, aligning with the filled circle at -10 and extension to the left.

So the answer is: $3x - 7 \leq -10$.

Answer

13. The speed limit sign on the expressway says that the speed limit is 55 mph. Write an inequality that represents all speeds you can legally drive on the expressway. (1 point) Responses x<55 x<55 x≤55 x is less than or equal to 55 x>55 x is greater than 55 x≥55

GPT-4o mini · Answer

The speed limit sign indicates that the maximum legal speed you can drive on the expressway is 55 mph. Therefore, you can drive at speeds less than or equal to 55 mph.

The appropriate inequality to represent this is:

\[ x \leq 55 \]

This means that $x$ (the speed you can drive) can be any value that is less than or equal to 55 mph.

So the correct response is: $x \leq 55$ (x is less than or equal to 55).

Answer

14. If you were to graph the inequality 35<7x on a number line:(2 points) Would you use an open or closed circle? Would your arrow on the number line point to the left or to the right?

GPT-4o mini · Answer

To analyze the inequality $35 < 7x$, we can first solve for $x$ by isolating it. 1. Divide both sides by 7: $$ \frac{35}{7} < x $$ This simplifies to: $$ 5 < x $$ or equivalently: $$ x > 5 $$ Now, let's determine how to graph this inequality: 1. **Open or Closed Circle:** Since the inequality is "greater than" (not inclusive), you would use an **open circle** at $5$. This indicates that $5$ is not included in the solution. 2. **Arrow Direction:** Since $x$ is greater than $5$, the arrow on the number line would point to the **right**. In summary: - **Open circle** at $5$ - **Arrow points to the right**. This means the graphical representation of the inequality $35 < 7x$ shows an open circle at the number 5 and an arrow extending to the right.