Solve each word problem algebraically.
13. The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers.
\[
\begin{array}{c}
(x+y)=(3 x)-1 \\
2 x=3 x-1 \\
3 x-3 x \\
-x=-1
\end{array}
\]
14. The len
more t
dimensi
inches.

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The two consecutive integers are \(\boxed{2}\) and \(\boxed{3}\).

Steps

Step 1 ：Let the two consecutive integers be x and x + 1.

Step 2 ：Write the equation: x + (x + 1) = 3x - 1.

Step 3 ：Simplify the equation: 2x + 1 = 3x - 1.

Step 4 ：Subtract 2x from both sides: 1 = x - 1.

Step 5 ：Add 1 to both sides: x = 2.

Step 6 ：Find the next consecutive integer: x + 1 = 2 + 1 = 3.

Step 7 ：Final Answer: The two consecutive integers are \(\boxed{2}\) and \(\boxed{3}\).