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Chapter 2: Q23. (page 100)

NUMBER THEORY Four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers.

Short Answer

Expert verified

The required integers are -4 and -2.

Step by step solution

01

Step 1. List the given data.

Four times the lesser of two consecutive even integers is 12 less than twice 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 xand the greater of them is x+2.

Translating the given condition into an equation,

03

Step 3. Solve the obtained equation.

Solving,

4x=2x+2鈭�12 (Given equation)

4x=2x+4鈭�12 (Distributive property)

4x=2x鈭�8 (Simplify)

4x鈭�2x=2x鈭�8鈭�2x (Subtract 2xfrom both sides)

2x=鈭�8 (Simplify)

2x2=鈭�82 (Divide both sides by 2)

x=鈭�4 (Simplify)

So, x=鈭�4is the solution of the given equation.

04

Step 4. Interpret the obtained solution.

The required integers were assumed to be x and x+2. It was obtained that for the given condition to be satisfied, .x=鈭�4 Then, the required integers are-4 and -2.

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Most popular questions from this chapter

Translate the following equation into a sentence:

4m=32

GEOMETRY Two rectangular walls each with a length of 12 feet and a width of 23 feet need to be painted. It costs \(0.08 per square foot for paint. How much will it cost to paint the walls?

F \)22.08 H \(34.50

G \)23.04 J $44 .16

Solve each equation. Check your solution.

5n+6=鈭�4

Translate each equation into a sentence.

32r-t3=132

Translate the following sentence into an equation:

鈥淭he quotient of t and forty is the same as twelve minus half of u鈥�.
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