Write Algebraic Expressions

Example corresponding to question 6 in algebra_1.

Example 1


Which of the following is the product of $1$ less than $4$ times $x$ and $3$ more that $5$ times $x$?

  1. $2x^2+7x+3$
  2. $(1-4x)(5x+3)$
  3. $20x^2$
  4. $20x^2+5$
  5. $2x^2+7x-3$

Solution



This example is about writing algebraic expressions given quantitative information.
  1. From the 5 possible solutions, we understand that we need to rewrite the given statements in the problem into one mathematical expression.

    We will first rewrite the problem as follows:

    Which of the following is the product of $1$ less than $4$ times $x$ and $3$ more that $5$ times $x$?

    The word product is important and means multiplication. The two expressions to multiply are: "$1$ less than $4$ times $x$" and "$3$ more that $5$ times $x$"

    We now translate the underlined expressions mathematically

    $1$ less than $4$ times $x$ is equivalent to $4x - 1$

    $3$ more that $5$ times $x$ is equivalent to $5x + 3$

    Finally the product is

    $(4x - 1)(5x+3)$

    Expand (multiply) to obtain

    $(4x - 1)(5x+3)= 20x^2+12x-5x-3 = 2x^2+7x-3$

    Answer E