Which of the following is the solution to the inequality below -6(4-x)<-4(x+1)

1 answer:

4 0

$-6(4-x) < -4(x+1)\ \ \ \ \ |\text{use distributive property}\\\\(-6)(4)+(-6)(-x) < (-4)(x)+(-4)(1)\\\\-24+6x < -4x-4\ \ \ \ \ \ |+24\\\\6x < -4x+20\ \ \ \ |+4x\\\\10x < 20\ \ \ \ \ |:10\\\\\boxed{x < 2}\\\\Answer:\ B.\ x < 2$

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3 years ago

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The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.

The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:

$A=w\cdot l$

For our rectangle w=12 in and l=20 in, the area is:

$\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}$

The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.

The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.

You can determine the value of x as follows: