PART A
The top of a table has dimensions 2 ft
by x+3 ft
and has an area of 8 ft2
.
Which of the following equations can be used to find the value of x
for this situation?
Responses
A 2x+3=8
B 2(x+3)=8
C 2x+5=8
D 2(2x+3)=8
To solve the equation 2(x+3)=8 for x, we can follow these steps:
1. Distribute the 2 to the terms inside the parentheses:
2x + 6 = 8
2. Subtract 6 from both sides of the equation to isolate the variable x:
2x = 8 - 6
2x = 2
3. Divide both sides of the equation by 2 to solve for x:
x = 2/2
x = 1
Therefore, the value of x is 1.
We can use the formula for the area of a rectangle to solve for x: A = length * width.
Given that the area is 8 ft^2, the length is 2 ft, and the width is x+3 ft, we can set up the equation as:
8 = 2 * (x+3)
Therefore, the equation that can be used to find the value of x is option B: 2(x+3)=8.
PART B
Solve the equation for x
.
To solve this problem, we need to find the value of x that satisfies the given conditions. The top of the table has dimensions 2 ft by x+3 ft, and its area is 8 ft^2.
The formula for the area of a rectangle is length multiplied by width.
In this case, we can set up the following equation to represent the area of the table:
Area = length * width
8 = 2 * (x + 3)
This equation can be simplified to:
8 = 2x + 6
To solve for x, we can isolate the variable by subtracting 6 from both sides of the equation:
8 - 6 = 2x
2 = 2x
Finally, we can solve for x by dividing both sides of the equation by 2:
1 = x
Therefore, the value of x that satisfies the given conditions is 1.
Looking at the given options, the correct equation that can be used to find the value of x for this situation is:
B. 2(x+3) = 8