Write an inequality for x that would give this rectangle an area of at least 246 it?. 8m (2x + 4)m

Question

asked Mar 14, 2020 199k views

2 Answers

MKroehnert · Answer 1 · 2020-03-20T15:00:43+0000

Question 1:

For this case we must solve the following expression:

$\frac {k} {3} + 4-2k = -9k$

Adding 9k to both sides of the equation we have:

$\frac {k} {3} + 4-2k + 9k = -9k + 9k\\\frac {k} {3} + 4 + 7k = 0$

Subtracting 4 from both sides of the equation:

$\frac {k} {3} + 4-4 + 7k = -4\\\frac {k} {3} + 7k = -4\\\frac {k + 21k} {3} = - 4\\\frac {22k} {3} = - 4\\$

Multiplying by 3 on both sides:

22k = -12

Dividing between 22 on both sides:

$k = \frac {-12} {22}\\k = - \frac {6} {11}$

Answer:

$k = - \frac {6} {11}$

Question 2:

For this case we have that by definition, the area of the rectangle is given by:

A = a * b

Where a and b are the sides of the rectangle.

If the area is at least
246ft ^ 2 we have:

$A \geq246$

That is to say:

$8 (2x + 4) \geq246\\16x + 32 \geq246\\16x \geq246-32\\16x \geq214\\x \geq \frac {214} {16}\\x \geq13.375$

Answer:

$x \geq13.375$