Q37. - Algebra 1

Question

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

Step-by-Step Solution

Answer

The required integers are $\mathbf{-}\mathbf{2}$ and 0.

Step 1. List the given data.

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

Step 2. Formulate the equation.

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

 

Translating the given condition into an equation,

 $3x=6\left(x+2\right)-6$

Step 3. Solve the obtained equation.

Solving,

$3x=6\left(x+2\right)-6$  (Given equation)

$3x=6x+12-6$  (Distributive property)

$3x=6x+6$  (Simplify)

$3x-6x=6x+6-6x$  (Subtract $6x$ from both sides)

$-3x=6$  (Simplify)

$\frac{-3x}{-3}=\frac{6}{-3}$  (Divide both sides by $-3$)

$x=-2$  (Simplify)

So, $x=-2$ is the solution of the given equation.

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, $x=-2$. Then, the required integers are $\mathbf{-}\mathbf{2}$ and 0.