Questions: 8. A board that is 22 inches long is cut into two pieces. The longer piece is 4 inches longer than the other piece. How long are the pieces?

Find the lengths of the two pieces of the board.

Define variables

Let's define:

• $x$ = length of the shorter piece (in inches)
• $x + 4$ = length of the longer piece (in inches)

Set up an equation based on the total length

The total length of the board is 22 inches, so: $x + (x + 4) = 22$

Solve the equation

$x + x + 4 = 22$ $2x + 4 = 22$ $2x = 18$ $x = 9$

Therefore:

• Shorter piece = $x = 9$ inches
• Longer piece = $x + 4 = 9 + 4 = 13$ inches

\(\boxed{\text{The pieces are 9 inches and 13 inches long}}\)

\(\boxed{\text{The pieces are 9 inches and 13 inches long}}\)