A rectangular frame has length (x+2) units and width (x-2) units. If the area is 96 square units, what is the value of x?

Please check the explanation.

Step-by-step explanation:

As we know that the area of a rectangle is defined by multiplying the length by the width.

Given

substituting all the given values in the formula to find the value of x.

subtract 96 from both sides

Putting x = -10 in the length and width will make the length and width negative, which can not be possible.

i.e.

length = l = x+2 = -10+2 = -8 units

width = w = x-2 = -10-2 = -12 units

Therefore, x=-10 must be excluded.

Now, putting the length of x = 10.

i.e.

length = l = 10+2 = 10+2 = 12 units

width = w = x-2 = 10-2 = 8

96 = 12 × 8

96 = 96

Therefore, the correct value of x = 10

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

hi! i think the answer is 1/2 : )