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Chapter 2: Q. 2.36 (page 119)

Find three consecutive even integers whose sum is-24.

Short Answer

Expert verified

Three consecutive integers are-10,-8,-6.

Step by step solution

01

Step 1. Assume three consecutive even integers.

Let three consecutive integers are,

1stinteger=n2ndinteger=n+23rdinteger=n+4

02

Step 2. Form the equation.

Question states that sum of three consecutive even integers is-24.

Equation for the statement will be,

n+(n+2)+(n+4)=-24

03

Step 3. Solve the equation.

Add like terms,

(n+n+n)+(2+4)=-243n+6=-24
04

Step 4. Isolate the variable.

Subtract6from each side of the equation,

(3n+6)-6=-24-6

3n=-30

05

Step 5. Simplify the equation.

Divide the equation by3.

3n3=-303n=-10
06

Step 6. Substitute n=-10 to find the integers.

1stinteger=n=-102ndinteger=n+2=-83rdinteger=n+4=-6

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