Question Solve the equation $5x + 2 = 12$ and use it to find the solution to an application problem.

Studdy Solution

STEP 1

Assumptions
1. We need to create a realistic scenario that can be modeled by the equation $5x + 2 = 12$ .
2. The variable $x$ will represent an unknown quantity we are trying to find.
3. The solution to the equation will provide the answer to the problem we create.

STEP 2

Let's create a context for the application problem. We can think of a situation where someone is buying multiple items that each cost the same amount, with an additional fixed cost.

STEP 3

Now, let's define the elements of the problem using the equation $5x + 2 = 12$ :
- $5x$ could represent the total cost of $x$ items, each costing $5 dollars. - The$ +2 $could represent an additional fixed cost, such as a delivery fee. - The$ =12$ represents the total amount spent.

STEP 4

Write the application problem using the context and elements defined in the previous steps.
Problem: Alex goes to a stationery store to buy pencils for his class. Each pencil costs $5. He also needs to pay a fixed delivery fee of$ 2. If Alex spends a total of $12, how many pencils did he buy?

STEP 5

To solve the problem, we need to solve the equation $5x + 2 = 12$ for $x$ .

STEP 6

Subtract 2 from both sides of the equation to isolate the term with $x$ .
$5x + 2 - 2 = 12 - 2$

STEP 7

Simplify both sides of the equation.
$5x = 10$

STEP 8

Divide both sides of the equation by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{10}{5}$

STEP 9

Simplify both sides to find the value of $x$ .
$x = 2$

STEP 10

Interpret the solution in the context of the problem.
Alex bought 2 pencils.

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Question Solve the equation $5x + 2 = 12$ and use it to find the solution to an application problem.

Studdy Solution

STEP 1

Assumptions
1. We need to create a realistic scenario that can be modeled by the equation $5x + 2 = 12$ .
2. The variable $x$ will represent an unknown quantity we are trying to find.
3. The solution to the equation will provide the answer to the problem we create.

STEP 2

Let's create a context for the application problem. We can think of a situation where someone is buying multiple items that each cost the same amount, with an additional fixed cost.

STEP 3

Now, let's define the elements of the problem using the equation $5x + 2 = 12$ :
- $5x$ could represent the total cost of $x$ items, each costing $5 dollars. - The$ +2 $could represent an additional fixed cost, such as a delivery fee. - The$ =12$ represents the total amount spent.

STEP 4

Write the application problem using the context and elements defined in the previous steps.
Problem: Alex goes to a stationery store to buy pencils for his class. Each pencil costs $5. He also needs to pay a fixed delivery fee of$ 2. If Alex spends a total of $12, how many pencils did he buy?

STEP 5

To solve the problem, we need to solve the equation $5x + 2 = 12$ for $x$ .

STEP 6

Subtract 2 from both sides of the equation to isolate the term with $x$ .
$5x + 2 - 2 = 12 - 2$

STEP 7

Simplify both sides of the equation.
$5x = 10$

STEP 8

Divide both sides of the equation by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{10}{5}$

STEP 9

Simplify both sides to find the value of $x$ .
$x = 2$

STEP 10

Interpret the solution in the context of the problem.
Alex bought 2 pencils.

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Question Solve the equation 5x+2=125x + 2 = 125x+2=12 and use it to find the solution to an application problem.

Studdy Solution

STEP 1

Assumptions1. We need to create a realistic scenario that can be modeled by the equation 5x+2=125x + 2 = 125x+2=12.2. The variable xxx will represent an unknown quantity we are trying to find.3. The solution to the equation will provide the answer to the problem we create.

STEP 2

Let's create a context for the application problem. We can think of a situation where someone is buying multiple items that each cost the same amount, with an additional fixed cost.

STEP 3

STEP 4

STEP 5

To solve the problem, we need to solve the equation 5x+2=125x + 2 = 125x+2=12 for xxx.

STEP 6

Subtract 2 from both sides of the equation to isolate the term with xxx.5x+2−2=12−25x + 2 - 2 = 12 - 25x+2−2=12−2

STEP 7

Simplify both sides of the equation.5x=105x = 105x=10

STEP 8

Divide both sides of the equation by 5 to solve for xxx.5x5=105\frac{5x}{5} = \frac{10}{5}55x​=510​

STEP 9

Simplify both sides to find the value of xxx.x=2x = 2x=2

STEP 10

Interpret the solution in the context of the problem.Alex bought 2 pencils.

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Studdy solves anything!

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Question Solve the equation $5x + 2 = 12$ and use it to find the solution to an application problem.

Assumptions
1. We need to create a realistic scenario that can be modeled by the equation $5x + 2 = 12$ .
2. The variable $x$ will represent an unknown quantity we are trying to find.
3. The solution to the equation will provide the answer to the problem we create.

To solve the problem, we need to solve the equation $5x + 2 = 12$ for $x$ .

Subtract 2 from both sides of the equation to isolate the term with $x$ .
$5x + 2 - 2 = 12 - 2$

Simplify both sides of the equation.
$5x = 10$

Divide both sides of the equation by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{10}{5}$

Simplify both sides to find the value of $x$ .
$x = 2$

Interpret the solution in the context of the problem.
Alex bought 2 pencils.