Graph the solution set of ineguality $$ -7.75 x+217-41 $$

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UpStudy AI · Accepted Answer

To graph the solution set of the inequality $$ -7.75x + 217 - 41 $$, we first need to simplify the expression and then determine the inequality.

1. **Simplify the expression:**
   $$
   -7.75x + 217 - 41 = -7.75x + 176
   $$

2. **Set up the inequality:**
   We need to express this as an inequality. For example, we can set it to be less than or equal to zero:
   $$
   -7.75x + 176 \leq 0
   $$

3. **Solve for $$ x $$:**
   Rearranging the inequality gives:
   $$
   -7.75x \leq -176
   $$
   Dividing both sides by -7.75 (remember to flip the inequality sign):
   $$
   x \geq \frac{176}{7.75}
   $$

Now, let's calculate $$ \frac{176}{7.75} $$ to find the critical point.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{176}{7.75}$$
- step1: Convert the expressions:
  $$\frac{176}{\frac{31}{4}}$$
- step2: Multiply by the reciprocal:
  $$176\times \frac{4}{31}$$
- step3: Multiply:
  $$\frac{176\times 4}{31}$$
- step4: Multiply:
  $$\frac{704}{31}$$
The critical point is calculated as follows:

$$
x \geq \frac{176}{7.75} \approx 22.71
$$

Now, we can graph the solution set of the inequality $$ -7.75x + 176 \leq 0 $$, which corresponds to $$ x \geq 22.71 $$.

### Graphing the Solution Set

1. **Draw a number line.**
2. **Mark the point $$ 22.71 $$ on the number line.**
3. **Since the inequality is $$ \geq $$, we will use a closed circle at $$ 22.71 $$ to indicate that this point is included in the solution set.**
4. **Shade the region to the right of $$ 22.71 $$ to indicate all values greater than or equal to $$ 22.71 $$.**

This represents the solution set of the inequality.
The solution set for the inequality $$ -7.75x + 176 \leq 0 $$ is all $$ x $$ values greater than or equal to approximately 22.71. On a number line, this is represented by a closed circle at 22.71 and shading to the right.

Graph the solution set of ineguality

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Graphing the Solution Set

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