Question

Write an equation and solve each problem.

Find four consecutive integers with the sum of $-142$.

Short answer

The required consecutive integers are $\mathbf{-}\mathbf{37}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{36}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{35}$ and $\mathbf{-}\mathbf{34}$.

Step-by-step solution

Step 1. List the given data.

The sum of four consecutive integers is$-142$.

Step 2. Write the equation for the given problem.

Let $x$be the first integer. Then, the four consecutive integers are $x$, $x+1$, $x+2$and $x+3$.

Translating the given problem into equation form,

$x+x+1+x+2+x+3=-142$

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

$x+x+1+x+2+x+3=-142$ (Obtained equation)

$4x+6=-142$ (Simplify)

$4x+6-6=-142-6$ (Subtract 6 from both sides)

$4x=-148$ (Simplify)

$\frac{4x}{4}=\frac{-148}{4}$ (Divide both sides by 4)

$x=-37$ (Simplify)

So, $x=-37$is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

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

Thus, the required consecutive integers are $\mathbf{-}\mathbf{37}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{36}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{35}$and localid="1642483245931" $\mathbf{-}\mathbf{34}$.