A student concluded that the inequality −3+2y≤4x is equivalent to the inequality y≥2x+32, as shown below. Describe and correct the student’s error.

And that's different from the claim of the student that:

The error of the student is that he/she changes the sign of the inequality from to and that's not possible since we don't multiply both sides of the equation by -1

Step-by-step explanation:

For this case we have the following inequality:

We want to rewrite the last expression with y in the left and x in the right so we can begin adding 3 in both sides of the inequality and we got:

Now we can divide both sides of the inequality by 2 and we got:

And that's different from the claim of the student that:

The error of the student is that he/she changes the sign of the inequality from to and that's not possible since we don't multiply both sides of the equation by -1

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!