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 \: = \: ( - 45)/( \: 3) \\`

`\bf \rightarrow \:x \: = \: \cancel( - 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.