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Example 1
Which of the following represents the product of $2$ more than $3$ times $x$ and $3$ less than twice $x$ ?
- $6x^2-5x+6$
- $6x^2-5x-6$
- $(3x+2)(3-2x)$
- $(3x+2)(2x+3)$
- $6x^2+5x+6$
Solution
This example is about writing algebraic expressions given quantitative information.
- According to the $5$ possible answers, we need to translate some of the information given in the problem into mathematical expressions. Let us first underline the most important information in this problem.
"Which of the following represents the product of $\underline{2}$ more than $\underline{3}$ times $\underline{x}$ and $\underline{3}$ less than twice $\underline{x}$?"
- Translate each underlined information in the problem into mathematical operator(s) and expressions
product means multiplication
$\underline{2}$ more than $\underline{3}$ times $\underline{x}$ is mathematically translated as $3x+2$
$\underline{3}$ less than twice $\underline{x}$ is mathematically translated as $2x-3$
- The final expression is mathematically translated as
$(3x+2)(2x-3)$
- The above expression in expanded form is equal to
$6x^2-5x-6$
Answer B
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