Rearranging Equations

The equation shown is used to find the force of gravity, F, between two objects, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.

$$F=\frac{Gm_1m_2}{r^2}$$

Which equation correctly shows the distance between the two objects?

An equation is given. y = 3x + c Create an equivalent equation by solving for x in terms of y and c.

(a)  

An equation is given.

$$A=4\pi r^2$$

Solve the equation for r.

This item has three parts. Eleanor incorrectly solves the equation $$\frac{1}{2}\left(x+18\right)=4\left(2x-6\right)-9x$$ .

Select the first equation in which Eleanor makes an error.

This item has three parts. Eleanor incorrectly solves the equation $$\frac{1}{2}\left(x+18\right)=4\left(2x-6\right)-9x$$ .

Create an equation to correct Eleanor's error identified in the previous question.

A sequence of steps for solving the equation 3(x − 2)​ = x + 4 is shown.

Move a property to each blank box to show the reason for each step.

Step: 3x − 6 = x + 4 Property: ​​ _​ (a)   ___

Step: 2x − 6 = 4 Property: _​ (b)   __

Step: 2x = 10 Property: _​ (c)   __

Step: x = 5 Property: _ (d)   __

The steps that a student took to solve the linear equation $$4x+5=31-\left(x-4\right)$$ are shown.

The student made an error in one of the steps.

Which step does the error appear?

What should be the solution to the original equation?

$$4x+5=31-\left(x-4\right)$$

x=_____