the larger of two consecutive integers is 7 greater than twice the smaller. find the intergers
Check my thinking on this.
n = smaller number
n+1= larger number
2n+7 = n+1
Solve for n.
To solve this problem, let's assign variables to represent the integers. Let's call the smaller integer "x" and the larger integer "x + 1" since they are consecutive.
According to the problem, the larger integer is 7 greater than twice the smaller integer. So we can write the equation:
x + 1 = 2x + 7
We subtract x from both sides to isolate the x variable:
1 = x + 7
Next, we subtract 7 from both sides:
-6 = x
Therefore, the smaller integer is -6.
To find the larger integer, we substitute the value of x into the expression x + 1:
-6 + 1 = -5
Therefore, the larger integer is -5.
So the integers are -6 and -5.