Question

Three consecutive integers have a sum of -42. Write and solve an equation to find the three integers.​

Answer 1

• Let the first integer be x.

• Let the second integer be x + 1 .

• Let the third integer be x + 2 .

According to the question

x + ( x + 1 ) + ( x + 2 ) = -42

Opening the brackets and simplifying :

x + x + 1 + x + 2 = -42

3x + 3 = -42

Now , solving equation :

$\bf \rightarrow \: \:3x \: + \: 3 \: = \: -42$

$\bf \rightarrow \: \: 3x \: = \: -42 \: - 3$

$\bf \rightarrow \:3x \: = \: -45 \:$

$\bf \rightarrow \:x \: = \: \frac{ - 45}{ \: 3}$

$\bf \rightarrow \:x \: = \: \cancel\frac{ - 45}{ \: 3} \: \: ^{ - 15}$

$\bf \rightarrow \:x \: = \: - 15$

${\boxed{ \Large{ \red{ \rm{ \underline{ Now \: \: substitute}}}}}}$

$\bf \implies \: \:x \: = \: - 15$

$\bf \implies \: \:x \: + \: 1 \: = \: - 15 \: + \: 1 \: = \: - 14$

$\bf \implies \: \:x \: + \:2 \: = \: - 15 \: + \: 2 \: = \: - 13$

-15 , -14 and -13 are the three consecutive integers.