Solved on Dec 05, 2023

Laura pumps water into an aquarium at 13 L/min. The aquarium starts with 25 L. Solve the inequality $13x+25 \leq 298$ for the number of minutes $x$ she pumps.

STEP 1

Assumptions
1. Laura is pumping water at a constant rate of 13 liters per minute.
2. The aquarium initially contains 25 liters of water.
3. The inequality $13x + 25 \leq 298$ represents the total volume of water in the aquarium after $x$ minutes, where $x$ is the number of minutes Laura pumps water into the aquarium.
4. The inequality must be solved for $x$ to determine the number of minutes Laura can pump water without exceeding 298 liters total in the aquarium.

STEP 2

First, we need to isolate the variable $x$ on one side of the inequality. We will start by subtracting 25 from both sides of the inequality to remove the initial volume of water from the equation.
$13x + 25 - 25 \leq 298 - 25$

STEP 3

Perform the subtraction to simplify the inequality.
$13x \leq 273$

STEP 4

Now, we will divide both sides of the inequality by 13 to solve for $x$ .
$\frac{13x}{13} \leq \frac{273}{13}$

STEP 5

Perform the division to find the value of $x$ .
$x \leq 21$

STEP 6

The inequality $x \leq 21$ means that Laura can pump water into the aquarium for up to 21 minutes without exceeding the total volume of 298 liters.

STEP 7

To graph the solution on the number line, we draw a number line and mark the point at $x = 21$ . Since the inequality includes the equal sign ( $\leq$ ), we will use a closed circle at 21 to indicate that 21 is part of the solution.

STEP 8

Draw an arrow to the left of the closed circle to indicate all numbers less than or equal to 21 are part of the solution set.

STEP 9

For part (b), we need to choose the statement that best describes the solution. The options are not provided in the problem, but based on the solution $x \leq 21$ , the statement would likely be something along the lines of "Laura can pump water into the aquarium for 21 minutes or less."
Laura can pump water into the aquarium for up to 21 minutes without exceeding the total volume of 298 liters. The solution on the number line is represented by a closed circle at 21 with an arrow pointing to the left, indicating all values up to and including 21.

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Laura pumps water into an aquarium at 13 L/min. The aquarium starts with 25 L. Solve the inequality $13x+25 \leq 298$ for the number of minutes $x$ she pumps.

STEP 1

STEP 2

First, we need to isolate the variable $x$ on one side of the inequality. We will start by subtracting 25 from both sides of the inequality to remove the initial volume of water from the equation.
$13x + 25 - 25 \leq 298 - 25$

STEP 3

Perform the subtraction to simplify the inequality.
$13x \leq 273$

STEP 4

Now, we will divide both sides of the inequality by 13 to solve for $x$ .
$\frac{13x}{13} \leq \frac{273}{13}$

STEP 5

Perform the division to find the value of $x$ .
$x \leq 21$

STEP 6

The inequality $x \leq 21$ means that Laura can pump water into the aquarium for up to 21 minutes without exceeding the total volume of 298 liters.

STEP 7

To graph the solution on the number line, we draw a number line and mark the point at $x = 21$ . Since the inequality includes the equal sign ( $\leq$ ), we will use a closed circle at 21 to indicate that 21 is part of the solution.

STEP 8

Draw an arrow to the left of the closed circle to indicate all numbers less than or equal to 21 are part of the solution set.

STEP 9

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Laura pumps water into an aquarium at 13 L/min. The aquarium starts with 25 L. Solve the inequality 13x+25≤29813x+25 \leq 29813x+25≤298 for the number of minutes xxx she pumps.

STEP 1

STEP 2

First, we need to isolate the variable xxx on one side of the inequality. We will start by subtracting 25 from both sides of the inequality to remove the initial volume of water from the equation.13x+25−25≤298−2513x + 25 - 25 \leq 298 - 2513x+25−25≤298−25

STEP 3

Perform the subtraction to simplify the inequality.13x≤27313x \leq 27313x≤273

STEP 4

Now, we will divide both sides of the inequality by 13 to solve for xxx.13x13≤27313\frac{13x}{13} \leq \frac{273}{13}1313x​≤13273​

STEP 5

Perform the division to find the value of xxx.x≤21x \leq 21x≤21

STEP 6

The inequality x≤21x \leq 21x≤21 means that Laura can pump water into the aquarium for up to 21 minutes without exceeding the total volume of 298 liters.

STEP 7

To graph the solution on the number line, we draw a number line and mark the point at x=21x = 21x=21. Since the inequality includes the equal sign (≤\leq≤), we will use a closed circle at 21 to indicate that 21 is part of the solution.

STEP 8

Draw an arrow to the left of the closed circle to indicate all numbers less than or equal to 21 are part of the solution set.

STEP 9

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Laura pumps water into an aquarium at 13 L/min. The aquarium starts with 25 L. Solve the inequality $13x+25 \leq 298$ for the number of minutes $x$ she pumps.

First, we need to isolate the variable $x$ on one side of the inequality. We will start by subtracting 25 from both sides of the inequality to remove the initial volume of water from the equation.
$13x + 25 - 25 \leq 298 - 25$

Perform the subtraction to simplify the inequality.
$13x \leq 273$

Now, we will divide both sides of the inequality by 13 to solve for $x$ .
$\frac{13x}{13} \leq \frac{273}{13}$

Perform the division to find the value of $x$ .
$x \leq 21$

The inequality $x \leq 21$ means that Laura can pump water into the aquarium for up to 21 minutes without exceeding the total volume of 298 liters.

To graph the solution on the number line, we draw a number line and mark the point at $x = 21$ . Since the inequality includes the equal sign ( $\leq$ ), we will use a closed circle at 21 to indicate that 21 is part of the solution.