Question

Write an equation and solve each problem.

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

Short answer

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

Step-by-step solution

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 $\mathbf{-}\mathbf{26}$.