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Chapter 8: Problem 41

Solve. $$ 3.5 \cdot q=0.2142 $$

Short Answer

Expert verified
q = 0.0612

Step by step solution

01

- Isolate the variable

To isolate the variable, divide both sides of the equation by the coefficient of the variable. So, divide both sides by 3.5.
02

- Perform the division

Calculate \ \( q = \frac{0.2142}{3.5}\ \).
03

- Simplify the fraction

Perform the division: \ \( q = 0.0612 \ \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the variable
When solving linear equations, the goal is to find the value of the variable. To do this, we need to move everything else to the other side of the equation. This process is called isolating the variable. In this exercise, the variable is q and it is currently being multiplied by 3.5. To isolate q, we need to get rid of the coefficient (3.5) by performing the opposite operation. Since 3.5 is multiplying q, we will divide both sides of the equation by 3.5.
This gives us the equation: \( q = \frac{0.2142}{3.5} \). Now, q is by itself on one side of the equation.
Division in equations
Dividing both sides of an equation by the same number is an essential step in solving for the variable. This keeps the equation balanced and ensures that we get the correct solution. In our example, after isolating the variable, we had the equation: \( q = \frac{0.2142}{3.5} \).

Performing the division means calculating what 0.2142 divided by 3.5 equals. When we divide these numbers, we find that the value of q is: \( q = 0.0612 \).
Remembering to divide both sides equally is key to maintaining the balance of the equation.
Simplifying fractions
Simplifying fractions means making the fraction as simple as possible. This often involves reducing it to the smallest terms. In our original division task, we simplified the fraction \( \frac{0.2142}{3.5} \) directly.

Sometimes, especially with more complex fractions or when the numerator and denominator share common factors, you might need to break down the numbers. Here, the fraction simplifies straightforwardly to 0.0612, which means it's already in its simplest form.
Simplifying fractions is a crucial step in solving equations, ensuring that the final answer is clear and easy to understand.

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Most popular questions from this chapter

Complete. 4 hr = _______sec

Many people leave the water running while they are brushing their teeth. Suppose that one person wastes 32 oz of water in this way each day. How much water, in gallons, is wasted by one person in a week? in a month ( 30 days)? in a year ( 365 days)? Assuming each of the 327 million people in the United States wastes water in this way, estimate how much water is wasted in the United States in a day; in a year.

\(0.401 \mathrm{~mL}=\) __________ \(\mathrm{L}\)

Convert to percent notation. 0.452

Multiply: \(8.03 \times 0.001\)
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