Question

On Saturdays, Jason mows yards and washes cars. He charges $25 per yard and an additional cost for each car he washes. Last Saturday, Jason mowed 5 yards and washed 10 cars. He made a total of $225, and the equation `5(25)+10x=225` describes the amount of money he made that Saturday. What does the variable `x` represent in this situation?

yards mowed

cars washed

each yard mowed

each car washed
Answer
Select the ordered pair(s) that are solutions to equation below:



`2x+3y=-12`
Answer
Solve and graph this inequality:



`-3x-1\ge11`
Answer
Solve and graph this inequality:



`\frac{1}{4}x+3>-10`
Answer
Solve and graph this inequality:



`-5\left(x+2\right)\ge-45`
Answer
A town's high temperature for a given month is 88°F and the low temperature is 65°F. Which compound inequality represents the range of temperatures for the given month?
Answered by GPT-4o mini
In the equation \( 5(25) + 10x = 225 \), the variable \( x \) represents the charge for washing each car. Therefore, the correct answer is:

**each car washed**
Answered by GPT-4o mini
To find the ordered pairs \((x, y)\) that are solutions to the equation \(2x + 3y = -12\), we can plug in various values for \(x\) and solve for \(y\), or vice versa.

### Let's find a few solutions:

1. **Let \(x = 0\):**
\[
2(0) + 3y = -12 \implies 3y = -12 \implies y = -4
\]
Solution: \((0, -4)\)

2. **Let \(x = -6\):**
\[
2(-6) + 3y = -12 \implies -12 + 3y = -12 \implies 3y = 0 \implies y = 0
\]
Solution: \((-6, 0)\)

3. **Let \(x = -3\):**
\[
2(-3) + 3y = -12 \implies -6 + 3y = -12 \implies 3y = -6 \implies y = -2
\]
Solution: \((-3, -2)\)

4. **Let \(y = -2\):**
\[
2x + 3(-2) = -12 \implies 2x - 6 = -12 \implies 2x = -6 \implies x = -3
\]
This is the same solution we already found: \((-3, -2)\).

### Summary of the solutions found:
- \((0, -4)\)
- \((-6, 0)\)
- \((-3, -2)\)

You can choose any of these ordered pairs or continue to find more by using different values for \(x\) or \(y\).
Answered by GPT-4o mini
To solve the inequality \(-3x - 1 \ge 11\), follow these steps:

### Step 1: Isolate the variable term
Add 1 to both sides:

\[
-3x - 1 + 1 \ge 11 + 1
\]

This simplifies to:

\[
-3x \ge 12
\]

### Step 2: Solve for \(x\)
Next, divide both sides by \(-3\). Remember, when dividing or multiplying both sides of an inequality by a negative number, you must flip the inequality sign:

\[
x \le -4
\]

### Step 3: Graph the solution
To graph the solution \(x \le -4\):

1. Draw a number line.
2. Locate the point \(-4\) on the number line.
3. Since the inequality is less than or equal to (\(\le\)), you will use a closed circle at \(-4\) to indicate that \(-4\) is included in the solution set.
4. Shade all the region to the left of \(-4\) to indicate all values less than \(-4\).

### Graph visualization:

```
<----------●====>
-4
```

This indicates that all values of \(x\) less than or equal to \(-4\) are part of the solution.
Answered by GPT-4o mini
To solve the inequality \(\frac{1}{4}x + 3 > -10\), follow these steps:

### Step 1: Isolate the variable term
Subtract 3 from both sides:

\[
\frac{1}{4}x + 3 - 3 > -10 - 3
\]

This simplifies to:

\[
\frac{1}{4}x > -13
\]

### Step 2: Solve for \(x\)
Next, multiply both sides by \(4\) to eliminate the fraction:

\[
4 \cdot \frac{1}{4}x > 4 \cdot -13
\]

This simplifies to:

\[
x > -52
\]

### Step 3: Graph the solution
To graph the solution \(x > -52\):

1. Draw a number line.
2. Locate the point \(-52\) on the number line.
3. Since the inequality is greater than (\(>\)), you will use an open circle at \(-52\) to indicate that \(-52\) is not included in the solution set.
4. Shade all the region to the right of \(-52\) to indicate all values greater than \(-52\).

### Graph visualization:

```
<====○---------->
-52
```

This demonstrates that the solution includes all values of \(x\) that are greater than \(-52\).
Answered by GPT-4o mini
To solve the inequality \(-5(x + 2) \ge -45\), follow these steps:

### Step 1: Distribute the -5
Distributing \(-5\) gives:

\[
-5x - 10 \ge -45
\]

### Step 2: Isolate the variable term
Add 10 to both sides:

\[
-5x - 10 + 10 \ge -45 + 10
\]

This simplifies to:

\[
-5x \ge -35
\]

### Step 3: Solve for \(x\)
Now, divide both sides by \(-5\). Remember to flip the inequality sign when dividing by a negative number:

\[
x \le 7
\]

### Step 4: Graph the solution
To graph the solution \(x \le 7\):

1. Draw a number line.
2. Locate the point \(7\) on the number line.
3. Since the inequality is less than or equal to (\(\le\)), use a closed circle at \(7\) to indicate that \(7\) is included in the solution set.
4. Shade all the region to the left of \(7\) to indicate all values less than or equal to \(7\).

### Graph visualization:

```
<----------●====>
7
```

This indicates that the solution includes all values of \(x\) that are less than or equal to \(7\).
Answered by GPT-4o mini
To represent the range of temperatures for the given month, where the high temperature is 88°F and the low temperature is 65°F, we can set up a compound inequality that shows that the temperature \( T \) lies between the low temperature and the high temperature.

The compound inequality can be expressed as:

\[
65 \leq T \leq 88
\]

This means that the temperature \( T \) is greater than or equal to 65°F and less than or equal to 88°F.