Question

question 1 points 3 cut a 10 ft long piece of wood into two pieces, so that one piece is 2 ft longer than the other. which of the following equations depicts the given situation? $x/2 = 10$ $x + 2 = 10$ $x = 10 + 2$ $2(x + 1) = 10$

Explanation:

Step1: Define the variables

Let the length of the shorter piece be \( x \) feet. Then the length of the longer piece is \( x + 2 \) feet (since it is 2 ft longer than the shorter one).

Step2: Set up the equation

The total length of the wood is 10 ft, which is the sum of the lengths of the two pieces. So, the equation is \( x+(x + 2)=10 \), which simplifies to \( x+2 + x=10 \) or \( 2x+2 = 10 \)? Wait, no, wait. Wait, the options: let's check the options again. Wait, the options are:

1. \( \frac{x}{2}=10 \)
2. \( x + 2=10 \)
3. \( x=10 + 2 \)
4. \( 2(x + 1)=10 \)

Wait, maybe I misdefined. Wait, maybe the shorter piece is \( x \), longer is \( x + 2 \), so total length \( x+(x + 2)=10 \), which is \( 2x+2 = 10 \), but that's not an option? Wait, no, the fourth option is \( 2(x + 1)=10 \), which is equivalent to \( 2x+2 = 10 \). Wait, let's re - examine.

Wait, if we let the shorter piece be \( x \), longer is \( x + 2 \). Then \( x+(x + 2)=10\Rightarrow2x + 2=10\Rightarrow2(x + 1)=10 \). Let's check the options:

• Option 1: \( \frac{x}{2}=10 \): This would mean the length of half of \( x \) is 10, which has nothing to do with the problem.
• Option 2: \( x + 2=10 \): This would mean the longer piece is 10, but the total length is 10, so the shorter piece would be 0, which is impossible.
• Option 3: \( x=10 + 2 \): This would mean the shorter piece is longer than the total length, which is impossible.
• Option 4: \( 2(x + 1)=10 \): Let's solve it. \( 2(x + 1)=10\Rightarrow x + 1 = 5\Rightarrow x = 4 \). Then the longer piece is \( 4+2 = 6 \). And \( 4 + 6=10 \), which matches the total length of the wood.

Answer:

\( 2(x + 1)=10 \) (the fourth option)