18 is decreased by the sum of a number and 2. The result is 9 less than 3 times the number. Find the number.

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution to the problem:

The problem states: "18 is decreased by the sum of a number and 2. The result is 9 less than 3 times the number. Find the number."

Let the unknown number be $x$ .
"The sum of a number and 2" can be written as $(x + 2)$ .
"18 is decreased by the sum of a number and 2" translates to $18 - (x + 2)$ . This is the left side of our equation.
Formulate the right side of the equation.
"3 times the number" is $3x$ .
"9 less than 3 times the number" means $3x - 9$ . This is the right side of our equation.
Set up the full equation.
$18 - (x + 2) = 3x - 9$
Simplify the left side of the equation.
$18 - x - 2 = 3x - 9$ $16 - x = 3x - 9$
Gather $x$ terms on one side and constant terms on the other.
Add $x$ to both sides and add 9 to both sides.
$16 + 9 = 3x + x$ $25 = 4x$
Solve for $x$ by dividing both sides by 4.
$x = \frac{25}{4}$ $x = 6.25$
The number is $\text{6.25}$ .

Answer