Q26. - Algebra 1

Question

Write an equation and solve each problem.

Find three consecutive even integers with the sum of $-84$.

Step-by-Step Solution

Answer

The required consecutive even integers are $-30,-28$ and $-26$.

Step 1. List the given data.

The sum of three consecutive even integers is $-84$.

Step 2. Write the equation for the given problem.

Let $x$ be the first even integer. Then, the three consecutive even integers are $x$, $x+2$ and $x+4$.

 

Translating the given problem into equation form,

 

$x+x+2+x+4=-84$

 

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

 

$x+x+2+x+4=-84$  (Obtained equation)

 

$3x+6=-84$  (Simplify)

 

$3x+6-6=-84-6$  (Subtract 6 from both sides)

 

$3x=-90$  (Simplify)

 

$\frac{3x}{3}=\frac{-90}{3}$  (Divide both sides by 3)

 

$x=-30$  (Simplify)

 

So, $x=-30$ is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

According to the assumption, $x$ is the first of the three required consecutive even integers which satisfy the given problem.

 

Thus, the required consecutive even integers are $\mathbf{-}\mathbf{30}\mathbf{,}\mathbf{ }\mathbf{-}\mathbf{28}$ and $\mathbf{-}\mathbf{26}$.