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Chapter 2: Q37. (page 101)

NUMBER THEORY Three times the lesser of two consecutive even integers is 6 less than six times the greater number. Find the integers.

Short Answer

Expert verified

The required integers are -2 and0.

Step by step solution

01

Step 1. List the given data.

Three times the lesser of two consecutive even integers is 6 less than six times the greater number.

02

Step 2. Formulate the equation.

Let the two consecutive even integers be xand x+2. Then, the lesser of them is and the greater of them is x+2.

Translating the given condition into an equation,

3x=6x+2鈭�6

03

Step 3. Solve the obtained equation.

Solving,

3x=6x+2鈭�6 (Given equation)

3x=6x+12鈭�6 (Distributive property)

3x=6x+6 (Simplify)

3x鈭�6x=6x+6鈭�6x (Subtract 6xfrom both sides)

鈭�3x=6 (Simplify)

鈭�3x鈭�3=6鈭�3 (Divide both sides by -3)

x=鈭�2 (Simplify)

So, x=鈭�2is the solution of the given equation.

04

Step 4. Interpret the obtained solution.

The required integers were assumed to be xand x+2. It was obtained that for the given condition to be satisfied, x=-2. Then, the required integers are-2 and 0.

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