QuestionFind two consecutive integers where $3(x+1) = 5x - 7$ .

Studdy Solution

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.
$x +1 =5 +1$

STEP 9

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

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QuestionFind two consecutive integers where $3(x+1) = 5x - 7$ .

Studdy Solution

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.
$x +1 =5 +1$

STEP 9

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

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QuestionFind two consecutive integers where 3(x+1)=5x−73(x+1) = 5x - 73(x+1)=5x−7.

Studdy Solution

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 (5*x -7).(x+1)=5x−7(x+1) =5x -7(x+1)=5x−7

STEP 3

Expand the left side of the equation.3x+3=5x−73x +3 =5x -73x+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+3x -3x =7 +3x−3x=7+3

STEP 5

implify the equation.2x=102x =102x=10

STEP 6

olve for x.x=102x = \frac{10}{2}x=210​

STEP 7

Calculate the value of x.x=5x =5x=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+1x +1 =5 +1x+1=5+1

STEP 9

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

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QuestionFind two consecutive integers where $3(x+1) = 5x - 7$ .

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.

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).
$(x+1) =5x -7$

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

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

implify the equation.
$2x =10$

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

Calculate the value of x.
$x =5$

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.