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?

Question

yards mowed

cars washed

each yard mowed

each car washed

Answer 1

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

Answer 2

Select the ordered pair(s) that are solutions to equation below:

`2x+3y=-12`

Answer 3

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 $x=0$: $$2(0)+3y=-12⟹3y=-12⟹y=-4$$ Solution: $(0,-4)$

2. Let $x=-6$: $$2(-6)+3y=-12⟹-12+3y=-12⟹3y=0⟹y=0$$ Solution: $(-6,0)$

3. Let $x=-3$: $$2(-3)+3y=-12⟹-6+3y=-12⟹3y=-6⟹y=-2$$ Solution: $(-3,-2)$

4. Let $y=-2$: $$2x+3(-2)=-12⟹2x-6=-12⟹2x=-6⟹x=-3$$ 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 $y$.

Answer 4

Solve and graph this inequality:

`-3x-1\ge11`

Answer 5

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.

Answer 6

Solve and graph this inequality:

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

Answer 7

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 $-52$.

Answer 8

Solve and graph this inequality:

`-5\left(x+2\right)\ge-45`

Answer 9

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 $7$.

Answer 10

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?

Answer 11

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:

$$65\le T\le 88$$

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