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Chapter 10: Problem 45

Solve the equation. Check your solution. $$240=2 x$$

Short Answer

Expert verified
The solution to the equation is \(x = 120\)

Step by step solution

01

Write Down the Equation

Firstly, jot down the equation as it is given, \(240 = 2x\)
02

Isolate the variable x

Next, try to get x alone on one side of the equation. As it is currently being multiplied by 2, divide both sides of the equation by 2 to cancel out the multiplication. The equation then becomes \(x = \frac{240}{2}\)
03

Calculate the Value

Lastly, perform the division operation on the right side of the equation to find the value of x. Therefore, \(x = 120\)

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Key Concepts

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

Isolating Variables
In algebra, isolating variables is crucial for solving equations. To isolate a variable means to get the variable alone on one side of the equation. This process helps identify the variable's value. For example, consider the equation \(240 = 2x\). The variable \(x\) is being multiplied by 2.

To isolate \(x\), divide both sides of the equation by 2. This step cancels the multiplication. The updated equation becomes \(x = \frac{240}{2}\). Now, \(x\) is isolated, making it easy to solve for its value. By performing actions that keep the equation balanced, we ensure the variable stands alone and accurately depicts its value.
Checking Solutions
After solving an equation, always check your solution. This verification step confirms that the answer is correct. To do this, substitute the found value back into the original equation and check if both sides are equal.

For instance, in solving \(240 = 2x\), we found \(x = 120\). Substitute 120 back in place of \(x\) in the original equation: \(240 = 2(120)\). Simplifying the right side, you get \(240 = 240\). Since both sides are equal, the solution \(x = 120\) is correct. Checking your solutions not only validates your calculations but also helps reinforce understanding of solving equations.
Basic Arithmetic Operations
Basic arithmetic operations like addition, subtraction, multiplication, and division are fundamental in solving equations. They help manipulate the equation to isolate the variable. Consider the equation \(240 = 2x\). Here, the operation involved is multiplication by 2.

To solve for \(x\), division is used to counteract this multiplication. Dividing both sides by 2, you find \(x = \frac{240}{2}\). This arithmetic step simplifies the equation, making it solvable. Understanding and employing these operations accurately is essential in algebra. It ensures each step towards isolating the variable is logical and precise.

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Most popular questions from this chapter

THOUGHT PROVOKINOVrite a formula for the length of a circular arc. Justify your answer.

Telecommunication towers can be used to transmit cellular phone calls. A graph with units measured in kilometers shows towers at points \((0,0),(0,5),\) and \((6,3)\) . These towers have a range of about 3 kilometers. a Sketch a graph and locate the towers. Are there any locations that may receive calls from more than one tower? Explain your reasoning. b. The center of City \(\mathrm{A}\) is located at \((-2,2.5),\) and the center of City \(\mathrm{B}\) is located at \((5,4)\) . Each city has a radius of 1.5 kilometers. Which city seems to have better cell phone coverage? Explain your reasoning.

In Exercises 9鈥�11, use the given information to write the standard equation of the circle. (See Example 2.) The center is \((0,0),\) and a point on the circle is \((3,-7)\).

REASONING In Exercises \(25-30\) , determine whether a quadrilateral of the given type can always be inscribed inside a circle. Explain your reasoning. rectangle

When will two lines tangent to the same circle not intersect? Justify your answer.
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