Final answer:
To find the value of x in a rectangular frame with given area, use the formula A = length * width and solve the resulting equation.
Step-by-step explanation:
Let's solve the problem step by step.
The formula for the area of a rectangle is length multiplied by width: A = length * width.
In this case, the length is (x+2) units and the width is (x-4) units, so the equation becomes: 7 = (x+2)(x-4).
We can solve this equation by expanding it and simplifying: x^2 - 2x - 8 = 7.
Now, let's rearrange the equation to get it in standard form: x^2 - 2x - 15 = 0.
This equation can be factored as: (x - 5)(x + 3) = 0.
From this, we have two possible values for x: x = 5 and x = -3. However, the width of a rectangle cannot be negative, so the only valid solution is x = 5. Therefore, the value of x is 5.
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