QuestionFind three consecutive odd integers where the sum of the first two equals five times the third plus three: $x + (x + 2) = 5(x + 4) + 3$ .

Studdy Solution

STEP 1

Assumptions1. The integers are consecutive odd numbers. The sum of the smaller two is equal to five times the largest number increased by three

STEP 2

Let's denote the three consecutive odd integers as $x$ , $x+2$ , and $x+4$ . The reason we're adding2 is because we're dealing with odd numbers, and odd numbers are always2 units apart.

STEP 3

According to the problem, the sum of the smaller two integers is equal to five times the largest integer increased by three. We can write this as an equation $x + (x+2) =5(x+) +3$

STEP 4

Now, let's simplify the equation. First, simplify the left side of the equation $2x +2 =(x+4) +3$

STEP 5

Next, simplify the right side of the equation $2x +2 =5x +20 +3$

STEP 6

Further simplify the right side of the equation $2x +2 =5x +23$

STEP 7

Now, let's isolate $x$ by subtracting $2x$ from both sides of the equation $2 =3x +23$

STEP 8

Next, subtract23 from both sides of the equation to isolate $x$ $-21 =3x$

STEP 9

Finally, divide both sides of the equation by3 to solve for $x$ $x = -7$

STEP 10

Now that we have the value of $x$ , we can find the three consecutive odd integers. The first integer is $x$ , the second integer is $x+2$ , and the third integer is $x+4$ .

STEP 11

Plug in the value of $x$ to find the three consecutive odd integersFirst integer $x = -7$
Second integer $x+ = -7+ = -5$
Third integer $x+4 = -7+4 = -3$
The three consecutive odd integers are -7, -5, and -3.

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QuestionFind three consecutive odd integers where the sum of the first two equals five times the third plus three: $x + (x + 2) = 5(x + 4) + 3$ .

Studdy Solution

STEP 1

Assumptions1. The integers are consecutive odd numbers. The sum of the smaller two is equal to five times the largest number increased by three

STEP 2

Let's denote the three consecutive odd integers as $x$ , $x+2$ , and $x+4$ . The reason we're adding2 is because we're dealing with odd numbers, and odd numbers are always2 units apart.

STEP 3

According to the problem, the sum of the smaller two integers is equal to five times the largest integer increased by three. We can write this as an equation $x + (x+2) =5(x+) +3$

STEP 4

Now, let's simplify the equation. First, simplify the left side of the equation $2x +2 =(x+4) +3$

STEP 5

Next, simplify the right side of the equation $2x +2 =5x +20 +3$

STEP 6

Further simplify the right side of the equation $2x +2 =5x +23$

STEP 7

Now, let's isolate $x$ by subtracting $2x$ from both sides of the equation $2 =3x +23$

STEP 8

Next, subtract23 from both sides of the equation to isolate $x$ $-21 =3x$

STEP 9

Finally, divide both sides of the equation by3 to solve for $x$ $x = -7$

STEP 10

Now that we have the value of $x$ , we can find the three consecutive odd integers. The first integer is $x$ , the second integer is $x+2$ , and the third integer is $x+4$ .

STEP 11

Plug in the value of $x$ to find the three consecutive odd integersFirst integer $x = -7$
Second integer $x+ = -7+ = -5$
Third integer $x+4 = -7+4 = -3$
The three consecutive odd integers are -7, -5, and -3.

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QuestionFind three consecutive odd integers where the sum of the first two equals five times the third plus three: x+(x+2)=5(x+4)+3x + (x + 2) = 5(x + 4) + 3x+(x+2)=5(x+4)+3.

Studdy Solution

STEP 1

Assumptions1. The integers are consecutive odd numbers. The sum of the smaller two is equal to five times the largest number increased by three

STEP 2

Let's denote the three consecutive odd integers as xxx, x+2x+2x+2, and x+4x+4x+4. The reason we're adding2 is because we're dealing with odd numbers, and odd numbers are always2 units apart.

STEP 3

According to the problem, the sum of the smaller two integers is equal to five times the largest integer increased by three. We can write this as an equationx+(x+2)=5(x+)+3x + (x+2) =5(x+) +3x+(x+2)=5(x+)+3

STEP 4

Now, let's simplify the equation. First, simplify the left side of the equation2x+2=(x+4)+32x +2 =(x+4) +32x+2=(x+4)+3

STEP 5

Next, simplify the right side of the equation2x+2=5x+20+32x +2 =5x +20 +32x+2=5x+20+3

STEP 6

Further simplify the right side of the equation2x+2=5x+232x +2 =5x +232x+2=5x+23

STEP 7

Now, let's isolate xxx by subtracting 2x2x2x from both sides of the equation2=3x+232 =3x +232=3x+23

STEP 8

Next, subtract23 from both sides of the equation to isolate xxx−21=3x-21 =3x−21=3x

STEP 9

Finally, divide both sides of the equation by3 to solve for xxxx=−7x = -7x=−7

STEP 10

Now that we have the value of xxx, we can find the three consecutive odd integers. The first integer is xxx, the second integer is x+2x+2x+2, and the third integer is x+4x+4x+4.

STEP 11

Plug in the value of xxx to find the three consecutive odd integersFirst integer x=−7x = -7x=−7Second integer x+=−7+=−5x+ = -7+ = -5x+=−7+=−5Third integer x+4=−7+4=−3x+4 = -7+4 = -3x+4=−7+4=−3The three consecutive odd integers are -7, -5, and -3.

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QuestionFind three consecutive odd integers where the sum of the first two equals five times the third plus three: $x + (x + 2) = 5(x + 4) + 3$ .

Let's denote the three consecutive odd integers as $x$ , $x+2$ , and $x+4$ . The reason we're adding2 is because we're dealing with odd numbers, and odd numbers are always2 units apart.

According to the problem, the sum of the smaller two integers is equal to five times the largest integer increased by three. We can write this as an equation $x + (x+2) =5(x+) +3$

Now, let's simplify the equation. First, simplify the left side of the equation $2x +2 =(x+4) +3$

Next, simplify the right side of the equation $2x +2 =5x +20 +3$

Further simplify the right side of the equation $2x +2 =5x +23$

Now, let's isolate $x$ by subtracting $2x$ from both sides of the equation $2 =3x +23$

Next, subtract23 from both sides of the equation to isolate $x$ $-21 =3x$

Finally, divide both sides of the equation by3 to solve for $x$ $x = -7$

Now that we have the value of $x$ , we can find the three consecutive odd integers. The first integer is $x$ , the second integer is $x+2$ , and the third integer is $x+4$ .

Plug in the value of $x$ to find the three consecutive odd integersFirst integer $x = -7$
Second integer $x+ = -7+ = -5$
Third integer $x+4 = -7+4 = -3$
The three consecutive odd integers are -7, -5, and -3.