7 Times a number equals 3 less than 5 times that number. What is the number?

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Answer 1 · 2017-01-11T23:23:37

The number is $- \frac{3}{2}$ $-3/2$

First, let's define the number we are looking for as $n$ $n$ .

In mathematical terms "7 times as number" can be written as:

$7 \times n$ $7 xx n$ or $7 \cdot n$ $7 * n$ or we will use $7 n$ $7n$

In mathematical terms "3 less than 5 times that number" can be written as:

$5 n - 3$ $5n - 3$

If these two expressions are equal we can write:

$7 n = 5 n - 3$ $7n = 5n - 3$

We can now solve for $n$ $n$ :

$7 n - 5 n = 5 n - 3 - 5 n$ $7n - color(red)(5n) = 5n - 3 - color(red)(5n)$

$(7 - 5) n = 5 n - 5 n - 3$ $(7 - 5)n = 5n - color(red)(5n) - 3$

$2 n = 0 - 3$ $2n = 0 - 3$

$2 n = - 3$ $2n = -3$

$\frac{2 n}{2} = - \frac{3}{2}$ $(2n)/color(red)(2) = -3/color(red)(2)$

$(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = -3/2$

$n = -3/2$