The rectangle shown below has an area of 4(x+3) square units.
a. use the distributive property to write an equivalent expression for the rectangle's area.
b. if the dimensions of the rectangle are doubled, what is the area of the new rectangle in terms of x?
c. will the ratio of the area of the original rectangle to the area of the larger rectangle be the same for any positive of x? explain

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step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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