Question

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

Short answer

The required integers are $-4$ and $-2$.

Step-by-step solution

Step 1. List the given data.

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

Translating the given condition into an equation,

Step 3. Solve the obtained equation.

Solving,

$4x=2\left(x+2\right)-12$ (Given equation)

$4x=2x+4-12$ (Distributive property)

$4x=2x-8$ (Simplify)

$4x-2x=2x-8-2x$ (Subtract $2x$from both sides)

$2x=-8$ (Simplify)

$\frac{2x}{2}=\frac{-8}{2}$ (Divide both sides by 2)

$x=-4$ (Simplify)

So, $x=-4$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, .$x=-4$ Then, the required integers are$-4$ and $-2$.