A. Write an equation and solve it. 1. Six times a certain number decreased by two is four times the same…

Question

A. Write an equation and solve it. 1. Six times a certain number decreased by two is four times the same number increased by twelve. Find the number.

ScanSolve AI Tutor · Accepted Answer

Here's the solution for the next problem:

1. Six times a certain number decreased by two is four times the same number increased by twelve. Find the number.

Let the certain number be $x$ .
Translate the problem into an equation.
"Six times a certain number decreased by two" can be written as $6x - 2$ .
"Four times the same number increased by twelve" can be written as $4(x + 12)$ .
The problem states that these two expressions are equal.
$6x - 2 = 4(x + 12)$
Distribute the 4 on the right side of the equation.
$6x - 2 = 4x + 48$
Gather the $x$ terms on one side and the constant terms on the other side.
Subtract $4x$ from both sides:
$6x - 4x - 2 = 48$ $2x - 2 = 48$
Add 2 to both sides:
$2x = 48 + 2$ $2x = 50$
Solve for $x$ by dividing both sides by 2.
$x = \frac{50}{2}$ $x = 25$
The number is $\boxed{\text{25}}$ .

A. Write an equation and solve it. 1. Six times a certain number decreased by two is four times the same number increased by twelve. Find the number.