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Chapter 2: Problem 6

Translate the following into algebraic equations. The sum of 5 times some number and 6 is 20 .

Short Answer

Expert verified
The equation is \(5x + 6 = 20\).

Step by step solution

01

Define the Unknown Variable

First, we need to define what our unknown number is. We'll call this number \(x\).
02

Translate the First Part

The problem states '5 times some number', which means 5 multiplied by our unknown number \(x\). We can write this as \(5x\).
03

Translate the Second Part

Next in the problem, it says the sum of the above expression and 6. We express this as \(5x + 6\).
04

Translate the Entire Equation

Finally, the problem states this sum 'is 20'. This means it equals 20, so we write the equation \(5x + 6 = 20\).
05

Combine All Parts

Combine all parts in a single algebraic expression: the equation is \(5x + 6 = 20\).

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Key Concepts

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

Understanding the Unknown Variable
In algebra, we often use variables to represent unknown quantities in equations. This allows us to create a flexible model that can be used to solve various problems involving numbers. In our exercise, the unknown variable is described as 'some number'. We choose to represent this number with the letter \( x \). By using \( x \), we make it easier to perform mathematical manipulations and find the specific value that satisfies the condition given in the problem. Whenever you see a phrase like 'some number', it's a good idea to assign it a variable, as it helps in solving the equation easier.
Translating Words to Algebraic Equations
One of the key skills in algebra is translating word problems into algebraic equations. This skill allows us to transform a verbal statement into a mathematical form that we can solve.In the given exercise, we start with the phrase '5 times some number.' This tells us to multiply our unknown variable \( x \) by 5, which we write as \( 5x \). Next, the phrase 'the sum of 5 times some number and 6' tells us to add 6 to the expression we formulated, resulting in \( 5x + 6 \).Finally, the phrase 'is 20' translates to an equation by using the equals sign: \( 5x + 6 = 20 \). Understanding these translations helps in setting up the correct equation to work with.
Solving the Equation
Once we have our equation, \( 5x + 6 = 20 \), the next step is to solve it. Solving an equation means finding the value of the unknown variable that makes the equation true.Here's how you can solve this equation:
  • First, isolate the \( x \) term by subtracting 6 from both sides of the equation. This simplifies the equation to \( 5x = 14 \).
  • Next, divide both sides of the equation by 5 to solve for \( x \). This gives us \( x = \frac{14}{5} \) or \( x = 2.8 \).
By following these steps, you can determine the value of the unknown variable. Each operation keeps the equation balanced, ensuring that the solution is correct.

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Most popular questions from this chapter

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