5.4 Application i - translating from verbal to mathetical expressions

$$\underset{6+x}{\underbrace{\underset{6}{\underbrace{\text{six}}}\underset{+}{\underbrace{\text{more}\text{than}}}\underset{x}{\underbrace{\text{a}\text{number}}}}}.$$

$$\underset{15-x}{\underbrace{\underset{15}{\underbrace{\text{Fifteen}}}\underset{-}{\underbrace{\text{minus}}}\underset{x}{\underbrace{\text{a}\text{number}}}}}.$$

$$\underset{y-8}{\underbrace{\underset{y}{\underbrace{\text{A}\text{quantity}}}\underset{-}{\underbrace{\text{less}}}\underset{8}{\underbrace{\text{eight}}}}}.$$

$$\underset{2x=10}{\underbrace{\underset{2\cdot }{\underbrace{\text{Twice}}}\underset{x}{\underbrace{\text{a}\text{number}}}\underset{=}{\underbrace{\text{is}}}\underset{10}{\underbrace{\text{ten}\text{.}}}}}$$

$$\underset{\frac{1}{2}z=20}{\underbrace{\underset{\frac{\text{1}}{\text{2}}}{\underbrace{\text{One}\text{half}}}\underset{\cdot }{\underbrace{\text{of}}}\underset{\text{z}}{\underbrace{\text{a}\text{number}}}\underset{\text{=}}{\underbrace{\text{is}}}\underset{\text{20}}{\underbrace{\text{twenty}\text{.}}}}}$$

$$\underset{3y=5+2y}{\underbrace{\underset{3}{\underbrace{\text{Three}}}\underset{\cdot }{\underbrace{\text{times}}}\underset{y}{\underbrace{\text{a}\text{number}}}\underset{=}{\underbrace{\text{is}}}\underset{5}{\underbrace{\text{five}}}\underset{+}{\underbrace{\text{more}\text{than}}}\underset{2\cdot }{\underbrace{\text{twice}}}\underset{y}{\underbrace{\text{the}\text{same}\text{number}\text{.}}}}}$$

$$\underset{\frac{x}{5}-10=15}{\underbrace{\underset{(\mathrm{ x }÷5)}{\underbrace{\text{A}\text{number}\text{divided}\text{by}\text{five,}}}\underset{-}{\underbrace{\text{minus}}}\underset{10}{\underbrace{\text{ten,}}}\underset{=}{\underbrace{\text{is}}}\underset{15}{\underbrace{\text{fifteen}\text{.}}}}}$$

Commas set off terms.

$$\underset{\text{The}\text{wording}\text{indicates}\text{this}\text{is}\text{to}\text{be}\text{considered}\text{as}\text{a}\text{single}\text{quantity.}}{\underbrace{\underset{8}{\underbrace{\text{Eight}}}\underset{÷}{\underbrace{\text{divided}\text{by}}}\underset{(5+x)}{\underbrace{\text{five}\text{more}\text{than}\text{a}\text{number}}}\underset{=}{\underbrace{\text{is}}}\underset{10}{\underbrace{\text{ten}}}}}$$

$$\frac{8}{5+x}=10$$

$$\underset{x(10+x)=20}{\underbrace{\underset{x}{\underbrace{\text{A}\text{number}}}\underset{\cdot }{\underbrace{\text{multiplied}\text{by}}}\underset{(10+x)}{\underbrace{\text{ten}\text{more}\text{than}\text{itself}}}\underset{=}{\underbrace{\text{is}}}\underset{20}{\underbrace{\text{twenty}\text{.}}}}}$$

A number plus one is divided by three times the number minus twelve and the result is four.
$$\begin{array}{ccc}(x+1)÷(3\cdot x-12)& =& 4\\ \frac{x+1}{3x-12}& =& 4\end{array}$$
Notice that since the phrase "three times the number minus twelve" does not contain a comma, we get the expression $3x-12$ . If the phrase had appeared as "three times the number, minus twelve," the result would have been
$$\frac{x+1}{3x}-12=4$$