Question

I don't understand this problem. Could you please explain to me how to do this problem? Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers?

Answer 1

`-8\text{ and -6}`

Step-by-step explanation

Step 1

Let x represent the first number

as the numbers are consecutive even integers, the next number would be x+2

so, the numbers are

`x,\text{ and x+2}`

Also,we have

a)Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer, so

`3(x+2)=x-10`

Step 2

solve the equation

`\begin{gathered} 3(x+2)=x-10 \\ \text{apply distributive property} \\ 3x+6=x-10 \\ \text{subtract x in both sides} \\ 3x+6-x=x-10-x \\ 2x+6=-10 \\ \text{subtract 6 in both sides} \\ 2x+6-6=-10-6 \\ 2x=-16 \\ \text{divide both sides by 2} \\ (2x)/(2)=(-16)/(2) \\ x=-8 \end{gathered}`

so, the numbers are

`\begin{gathered} x=-8 \\ x+2=-8+2=-6 \end{gathered}`
`-8\text{ and -6}`

I hope this helps you