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The area of the shaded region is 118 ft².

Which equation can be used to find the value of x, in feet?

1) 15x - 16 = 118
2) 15x + 8 = 118
3) 15x + 32 = 118
4) 15x - 24 = 118

Answer :

To find the correct equation that can be used to determine the value of [tex]x[/tex] given that the area of the shaded region is 118 square feet, we need to analyze the given options.

When you look at these options, they are all of the form [tex]15x + b = 118[/tex]. Here, [tex]15x[/tex] appears to represent some component related to the area, and [tex]b[/tex] adjusts the equation to match the area of 118 square feet.

Each option can be broken down as follows:

  1. Equation 1: [tex]15x - 16 = 118[/tex]

    • Solving for [tex]x[/tex]: Add 16 to both sides:
    • [tex]15x = 118 + 16[/tex]
    • [tex]15x = 134[/tex]

  2. Equation 2: [tex]15x + 8 = 118[/tex]

    • Solving for [tex]x[/tex]: Subtract 8 from both sides:
    • [tex]15x = 118 - 8[/tex]
    • [tex]15x = 110[/tex]

  3. Equation 3: [tex]15x + 32 = 118[/tex]

    • Solving for [tex]x[/tex]: Subtract 32 from both sides:
    • [tex]15x = 118 - 32[/tex]
    • [tex]15x = 86[/tex]

  4. Equation 4: [tex]15x - 24 = 118[/tex]

    • Solving for [tex]x[/tex]: Add 24 to both sides:
    • [tex]15x = 118 + 24[/tex]
    • [tex]15x = 142[/tex]

The correct equation that matches the information given is the one that solves exactly for the area, implying that [tex]15x[/tex] equals the targeted value after solving.

The answer that correctly gives 118 square feet based on the balance between component [tex]15x[/tex] and constant [tex]b[/tex] is option 2:

Option 2: [tex]15x + 8 = 118[/tex]

This is because, when solved for [tex]x[/tex], it appropriately modifies [tex]15x[/tex] to equal 118 as specified by the problem.

Therefore, the correct equation is 15x + 8 = 118.

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