Math Snap

STEP 1

Assumptions1. We are looking for two consecutive integers.
. We denote the smaller integer as x.
3. The larger integer, being consecutive, is then x +1.

STEP 2

We write down the problem statement as an equation. According to the problem, three times the greater integer ((x+1)) is7 less than five times the lesser integer (5x -7).
$$(x+1) =5x -7$$

STEP 3

Expand the left side of the equation.
$$3x +3 =5x -7$$

STEP 4

Rearrange the equation to bring all terms involving x to one side and constants to the other side.
$$x -3x =7 +3$$

STEP 5

implify the equation.
$$2x =10$$

STEP 6

olve for x.
$$x = \frac{10}{2}$$

STEP 7

Calculate the value of x.
$$x =5$$

STEP 8

Now that we have the value of the smaller integer, we can find the larger integer by adding1 to x.
$$x +1 =5 +1$$

Calculate the value of the larger integer.
$$x + =6$$The two consecutive integers are5 and6.