Question

Use the description shown below. "Choose any number Add 10 to the number. Multiply the result by 2 Subtract 18 from the result. Multiply the result by one half Subtract the original number." Write a linear equation for the description. Let \(x\) represent the number that is chosen and let \(y\) represent the final result.

Short answer

The linear equation for the given problem is \(y = 1\).

Step-by-step solution

Assigning Variables

Start by interpreting the problem. Here \(x\) is the original number that is chosen and \(y\) will represent the final result according to the given problem.

Translation Into Mathematical Symbols

Translate each sentence into algebraic expressions. First, we choose any number, let it be \(x\). Then, add 10 to it (so, now we have \(x+10\)). We then multiply the result by 2. So, now it becomes \((x+10) \times 2\) or \(2x + 20\). Subtract 18 from it to get \(2x+20-18\) or \(2x+2\). We then multiply the result by one half (or divide by 2) to get \(2x+2 \div 2\) which is \(x+1\). Finally, we subtract the original number (or \(x\)) from our result. So, now we have \(x+1-x\) or \(1\) as our final result.

Writing the Linear Equation

We can represent the final result by \(y\). So, the linear equation for the given problem can be written as \(y = 1\).