To solve the problem, we need to identify the two consecutive integers based on the given conditions.
Let's denote the greater integer by [tex]\( x \)[/tex]. Since the integers are consecutive, the lesser integer will be [tex]\( x - 1 \)[/tex].
According to the problem, four times the greater integer is 18 more than three times the lesser integer. We can write this relationship as an equation:
[tex]\[ 4x = 18 + 3(x - 1) \][/tex]
Now, let's solve the equation step-by-step:
1. Distribute the 3 on the right side:
[tex]\[ 4x = 18 + 3x - 3 \][/tex]
2. Simplify the right side:
[tex]\[ 4x = 3x + 15 \][/tex]
3. Subtract [tex]\( 3x \)[/tex] from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ 4x - 3x = 15 \][/tex]
[tex]\[ x = 15 \][/tex]
So, the greater integer is [tex]\( 15 \)[/tex].
To find the lesser integer, subtract 1 from the greater integer:
[tex]\[ 15 - 1 = 14 \][/tex]
Thus, the two consecutive integers are:
[tex]\[ 15 \text{ and } 14 \][/tex]
