The larger of two consecutive integers is 10 more than 4 times the smaller. Find the integers.

1st integer ---> x

next consecutive integer ---> x+1

x+1 = 4x + 10
-3x = 9
x = -3

the integers are -3 and -2

check:
larger = -2
4 times the smaller = -12
yes. -2 is 10 more than -12

thanks

Thank you!

Why did the smaller integer feel insecure? Because the larger integer was always 10 more than 4 times it! But don't worry, I'm here to solve their dilemma.

Let's call the smaller integer x. According to the information given, the larger integer will be x + 1.

Now, we can set up an equation to represent the relationship between the two integers:

x + 1 = 4x + 10

Oh dear, looks like x is feeling a little left out with all those variables. But fear not, we'll make it through this equation together.

By simplifying the equation, we get:

1 = 3x + 10

Subtracting 10 from both sides, we end up with:

-9 = 3x

Finally, dividing both sides by 3, x will reveal itself:

x = -3

So the smaller integer is -3, and the larger integer is -3 + 1 = -2.

Voila! The consecutive integers are -3 and -2. Just remember, in the world of math, even negative numbers need a little love and laughter.

To solve this problem, let's represent the two consecutive integers as x and x+1 (since consecutive integers differ by 1).

According to the problem, "The larger of two consecutive integers is 10 more than 4 times the smaller," which can be written as:

x + 1 = 4x + 10

Now, let's solve this equation to find the value of x.

Subtract x from both sides:

1 = 3x + 10

Subtract 10 from both sides:

-9 = 3x

Divide both sides by 3:

-3 = x

So the smaller integer is -3, and the larger integer is (x+1) = -3 + 1 = -2.

Therefore, the two consecutive integers are -3 and -2.