Let's solve this problem step by step:
1. Identify the given information:
- The area of the rectangle is 91 square inches.
- The length of the rectangle is 1 less than twice its width.
2. Define the variables:
- Let [tex]\( w \)[/tex] be the width of the rectangle.
- Then the length of the rectangle is [tex]\( 2w - 1 \)[/tex].
3. Use the formula for the area of a rectangle:
- Area = Length [tex]\(\times\)[/tex] Width.
- So the equation becomes: [tex]\((2w - 1)w = 91\)[/tex].
4. Expand and simplify the equation:
- [tex]\((2w - 1)w = 91\)[/tex].
- [tex]\(2w^2 - w = 91\)[/tex].
5. Rearrange the equation into standard quadratic form [tex]\( ax^2 + bx + c = 0 \)[/tex]:
- Subtract 91 from both sides to set the equation to 0.
- [tex]\(2w^2 - w - 91 = 0\)[/tex].
So, the correct answers to fill in the blanks are:
[tex]$
2 \quad w^2 - \quad 1 \quad w + \quad (-91) = 0
$[/tex]
Hence, the equation that could be used to find the width of the rectangle, [tex]\( w \)[/tex], is [tex]\( 2w^2 - w - 91 = 0 \)[/tex].
