Use complete sentences to describe why it is necessary to do the same thing to both sides of an equation to perform valid operations

It is necessary to do the same thing to both sides of th equation to perform valid operations because your equation would change otherwise. If you do not do the same action on both sides, your equation will not stay the same as it started. One side could get too large or too small in amount for the other side.

Step-by-step explanation:

Take 2x + 7 = 6 for example. First, you would subtract 7 from both sides. Your new equation is 2x = -1. Then, divide two from both sides. The new equation is .

If you hadn't subtracted 7 from both sides, the equation wouldn't have stayed the same, and you wouldn't have gotten the correct answer. Your equation would have changed to 2x = 6. Your answer would be x = 3. These two equations are not the same.

This shows that it is necessary to do the same thing to both sides of the equation.

Hope it helps. Good Luck!

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .