Question

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

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.
Subtract 24 from both sides of the equation.

Divide both sides of the equation by 15.
Divide both sides of the equation by 15.
Question 7
12. Which inequality represents the graph below:



(1 point)
Responses

3x−7≤−10
3 x minus 7 is less than or equal to negative 10

−3x+7<10
−3x+7<10

3x+7>10
3 x plus 7 is greater than 10

−3x−7≥−10

Answer 1

Let's address each question one by one.

### Question 11:
**Original equation:**
\[ 3 - 15x + 24 + 16x = 4x - 24 - 4x \]

**Combining like terms on the left side:**
\[
(3 + 24) + (-15x + 16x) = 27 + 1x \text{ or just } x
\]

The left side simplifies to:
\[ 27 + x \]

**On the right side:**
\[ 4x - 24 - 4x = -24 \]

So the equation now looks like:
\[ 27 + x = -24 \]

**Next best step:**
To isolate \( x \), we should subtract 27 from both sides:
\[ 27 + x - 27 = -24 - 27 \]
\[ x = -51 \]

**The correct response is:**
**Subtract 27 from both sides of the equation.**

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### Question 12:
To solve for the inequality that represents a graph, it is essential to understand how parameters such as slope and y-intercept will display changes considering given boundaries. Without a visual of the graph, I can provide insight into how to analyze the expressions listed.

1. **3x − 7 ≤ −10** can be rearranged to show the relationships between values of \( x \) and constants.
2. **−3x + 7 < 10** rearranges to address values affecting \( x \).
3. **3x + 7 > 10** indicates positive slope, affecting inequality directions based on placement.
4. **−3x − 7 ≥ −10** requires analyzing values closely when shifted.

**Choosing the correct inequality** will depend on potential elements—either their slope or directionality. To determine the right choice without the visual is challenging.

If you can describe the graph (the direction of the line, shading, or points), I can provide a more accurate inference about which inequality to select based on your options offered.