So firstly, our two integers are x and x + 2. And we know that the sum of the smaller integer, x, and 3 times the larger integer, x + 2, is 150. Using what we know, our equation is [tex] x+3(x+2)=150 [/tex]
Firstly, foil 3(x + 2): [tex] x+3x+6=150 [/tex]
Next, combine like terms: [tex] 4x+6=150 [/tex]
Next, subtract 6 on both sides: [tex] 4x=144 [/tex]
And lastly, divide 4 on both sides and your answer will be [tex] x=36 [/tex]
Now since we know that the smaller integer is 36, add 2 to 36 to get the larger integer, which is 38.
In short, the smaller integer is 36 and the larger integer is 38.
