Simplifying and factoring linear expressions Transitional Reasoning Practice

Questions

1. 1.

   A landscaping crew is enclosing a rectangular community garden that has a length of $4(2x + 3)$ meters and a width of $3(x - 1)$ meters. The entire perimeter will be fenced except for an access walkway of length $(6x - 10)$ meters. Which of the following expressions represents the total length of fencing required, in meters, in completely factored form?

   • A) $8(2x + 1)$
   • B) $2(8x + 14)$
   • C) $4(4x + 7)$
   • D) $4(4x - 7)$
2. 2.

   An art instructor prepares 6 identical craft kits for a workshop. Each kit contains 4 wooden dowels of length $2x + 3$ centimeters and 3 metal rods of length $3x - 2$ centimeters, after which a trimmed piece of $x - 4$ centimeters is cut off and removed from each kit. Which of the following expressions represents the total length of the remaining materials across all 6 kits in completely factored form?

   • A) $6(16x + 10)$
   • B) $12(8x + 1)$
   • C) $12(8x + 5)$
   • D) $6(17x + 6)$

Answers and step-by-step solutions appear after you finish the test.