the larger of two consecutive integers is 10 more than 4 times the smaller find the interger

Let the two consecutive integers be \( x \) (the smaller integer) and \( x + 1 \) (the larger integer).

According to the problem, the larger integer is 10 more than 4 times the smaller integer. This gives us the equation:

\[
x + 1 = 4x + 10
\]

Now, solve for \( x \):

\[
x + 1 = 4x + 10
\]

Subtract \( x \) from both sides:

\[
1 = 3x + 10
\]

Now, subtract 10 from both sides:

\[
1 - 10 = 3x
\]

\[
-9 = 3x
\]

Now, divide both sides by 3:

\[
x = -3
\]

So the smaller integer is \( -3 \), and the larger integer is:

\[
x + 1 = -3 + 1 = -2
\]

Thus, the two consecutive integers are \( -3 \) and \( -2 \).

Would you like further explanation or details on this? Here are some related questions:

1. How would the equation change if the larger integer were 5 more than 3 times the smaller?
2. What if the difference between the two integers was given instead?
3. Can you solve for integers where the larger is a fraction more than the smaller?
4. How does the problem change if the integers are not consecutive?
5. What are other methods to check the solution?

**Tip:** For consecutive integers, always set up variables in terms of \( x \) and \( x+1 \).

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

Learn how to solve the problem where the larger of two consecutive integers is 10 more than 4 times the smaller. This problem covers algebraic concepts like consecutive integers and solving linear equations, suitable for Grades 6-8 students.

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