Problem 111
Question
Translate from English to an algebraic expression or equation, whichever is appropriate. Let the variable \(x\) represent the number. The product of \(\frac{2}{3}\) and a number increased by 6
Step-by-Step Solution
Verified Answer
The algebraic expression for the given word problem is \(\frac{2}{3}x + 6\).
1Step 1: Identify the unknown and other elements
First, it is known that \(x\) is the unknown variable which represents the number. The phrases used are 'product', which stands for multiplication, and 'increased by', which stands for addition.
2Step 2: Translate English phrases into mathematical operations
Next, the phrase 'the product of \(\frac{2}{3}\) and a number' can be translated into the multiplication of the number by \(\frac{2}{3}\), which is \(\frac{2}{3}x\). 'Increased by 6' translates into '+6'.
3Step 3: Combine the mathematical operations into an algebraic expression
Combining the two mathematical operations obtained from the translation, the algebraic expression becomes \(\frac{2}{3}x + 6\).
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