Q29. - Algebra 1

Question

Write an equation and solve each problem.

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

Step-by-Step Solution

Answer

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

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 $\mathbf{-}\mathbf{34}$.