Q10. - Algebra 1

Question

Write an equation and solve each problem. Find three consecutive integers with a sum of $-36$.

Step-by-Step Solution

Answer

The equation of a given situation is $x+(x+1)+(x+2)$.

The three consecutive integers whose sum is $-36$ are $-11,-12,\mathrm{and}13$.

Step 1. Make the equation.

The sum of three consecutive integers is $-36$.

Assume that the smallest integer be x.

So, the equation is $x+(x+1)+(x+2)$

Step 2. Find the value of x from the equation.

$\begin{array}{l}x+(x+1)+(x+2)=-36\\ x+x+1+x+2=-36\\ 3x+3=-36\\ 3x=-36-3\\ 3x=-39\\ x=\frac{-39}{3}\\ x=-13\end{array}$

Step 3. Write three consecutive integers.

The three consecutive integers are $-13$, $-13+1=-12$ and $-13+2=-11$.