# Five less than 6 times a number is the same as the number plus 10. What is the number?

Dec 1, 2017

3

#### Explanation:

From the question, you get an expression of $6 n - 5 = n + 10$

Move all $n$ terms to one side and number terms to the other

$6 n - 5 = n + 10$

$5 n = 15$

Isolate $n$

$\frac{5 n}{5} = \frac{15}{5}$

$n = 3$

Dec 1, 2017

The number is 3

#### Explanation:

Problems like this are confusing because it's hard to write an algebra expression for concepts like "five less than 6 times a number,"

The trick is to write that amount one step at a time.

1) Let $x$ be the number

The number . . . . . . $x$ $\leftarrow$ the number

2) Now find a way to write "six times the number"
In algebra, that is "$6 \times x ,$" written as $6 x$

So far, you have
The number . . . . . . . . . . $x$ $\leftarrow$ the number
6 times the number . . $6 x$

3) Now find the way to write "5 less than that"
In algebra, that is "$6 x$ minus 5," written as $6 x - 5$

So now you have
The number . . . . . . . . . . $x$ $\leftarrow$ the number
6 times the number . . $6 x$
5 less than that . . . . . . $6 x - 5$ $\leftarrow$ "5 less than 6 times a number"

The problem says that $6 x - 5$ is the same as another amount.

That other amount is "the number plus 10"

So find a way to express the concept "the number plus 10"
Do this one step at a time

The number . . . . . $x$ $\leftarrow$ the number
plus 10 . . . . . . . . . $x + 10$ $\leftarrow$ the number plus 10
....................................

Now you can write an equation you can solve because you turned the words of the problem into algebra.

1) "Five less than 6 times a number"
.$6 x - 5$

2) "is the same as"
$=$

3) "the number plus 10"
$x + 10$

Putting it all together, you have
$6 x - 5$$=$ $x + 10$
..................................................

$6 x - 5$$=$ $x + 10$
Solve for $x$, already defined as "the number"

1) Subtract $x$ from both sides to get all the $x$ terms on the same side
$5 x - 5 = 10$

2) Add 5 to both sides to isolate the $5 x$ term
$5 x = 15$

3) Divide both sides by 5 to isolate $x$, already defined as "the number"
$x = 3$ $\leftarrow$ answer