solve the equation in two different ways. Show all the steps. Finally, choose which solution method you liked best and explain your reason. 8(x+9)=144

Answer 1

Solution method 1: Distributive Property and Isolation of x
First, we will apply the distributive property by multiplying 8 with both terms inside the parentheses:
8(x+9) = 8*x + 8*9
Simplifying each term:
8x + 72 = 144

Next, we will isolate x by subtracting 72 from both sides of the equation:
8x + 72 - 72 = 144 - 72
Simplifying:
8x = 72

To find the value of x, divide both sides of the equation by 8:
8x/8 = 72/8
Simplifying:
x = 9

Solution method 2: Application of Reverse Operations
Starting with the original equation:
8(x+9)=144

We can start solving by simplifying the equation within the parentheses by applying the distributive property:
8x + 72 = 144

Next, we will isolate x by subtracting 72 from both sides of the equation:
8x = 144 - 72
Simplifying:
8x = 72

Lastly, divide both sides of the equation by 8 to find the value of x:
8x/8 = 72/8
Simplifying:
x = 9

I preferred solution method 1, which involved using the distributive property and isolating x. This way allowed me to see the intermediate steps and how the equation was simplified at each stage. It also provided clarity when isolating x using the reverse operations. Solution method 2, while valid, involved inverting the order of some operations, which could potentially lead to errors if not done carefully.

Answer 2

I need another way

Answer 3

Certainly! Here's an alternative method to solve the equation:

8(x+9)=144

First, divide both sides of the equation by 8 to isolate the expression within the parentheses:
(x+9) = 144/8
(x+9) = 18

Next, subtract 9 from both sides of the equation to get x by itself:
x = 18 - 9
x = 9

In this method, we directly divide both sides of the equation by 8 at the beginning, rather than distributing 8 and then isolating x. This approach allows us to immediately solve for x without going through as many steps. However, it's important to note that this method relies on recognizing that dividing both sides by 8 will "cancel out" the multiplication in the equation and simplify the expression.

Answer 4

Does / mean division

Answer 5

Yes, the symbol "/" represents division in mathematics.