Question

The sum of three consecutive even integers is 36. Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.
Which equation can be used to find the first integer?

A)3x = 2x + 6

B)3x + 6 = 36

C)3x + 36 = 2x + 6

D)2x + 6 = 36

Answer 1

Let

x------>  the first even integer

x+2---->the second even integer

x+3---->the third even integer

we know that

$x+(x+2)+(x+4)=36$ -----> equation that represent the situation

solve for x

Combine like terms in the left side

$(x+x+x)+(2+4)=36$

$3x+6=36$

therefore

the answer is the option B

$3x+6=36$

Answer 2

The equation that can be used to find the first integer is B) 3x + 6 = 36

Further explanation

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

$\large {m = \frac{y_2 - y_1}{x_2 - x_1}}$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\boxed {y - y_1 = m ( x - x_1 )}$

Let us tackle the problem.

Given:

The First Integer = x

The Second Integer = x + 2

The Third Integer = x + 4

The sum of three consecutive even integers is 36.

$\texttt{The First Integer + The Second Integer + The Third Integer = 36}$

$x + (x + 2) + (x + 4) = 36$

$x + x + x + 2 + 4 = 36$

$\large {\boxed {3x + 6 = 36} }$

Learn more

• Infinite Number of Solutions : brainly.com/question/5450548
• System of Equations : brainly.com/question/1995493
• System of Linear equations : brainly.com/question/3291576

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point