Half of the sum of x and 6.2 is the same as 19.6 less than x. Create and solve an equation to find x.

Question

Please explain all your steps.

Answer 1

Hello, thank you for taking the time to post your question!

The word problem given in the question can be translated into this equation

(x + 6.2)/2 = x – 19.6

From there then it would just be a matter of solving for the value of “x” algebraically

x + 6.2 = (x – 19.6)*2

x + 6.2 = 2x – 39.2

45.4  = x

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

We can translate the problem statement into an equation as follows:

(1/2)(x + 6.2) = x - 19.6

To solve for x, we can begin by simplifying both sides of the equation:

First, we can distribute the 1/2 on the left-hand side:

1/2 * x + 1/2 * 6.2 = x - 19.6

Then, we can combine like terms:

1/2 * x + 3.1 = x - 19.6

Next, we can isolate the variable terms on one side and the constant terms on the other side:

1/2 * x - x = -19.6 - 3.1

Simplifying the left-hand side by combining like terms, we get:

-1/2 * x = -22.7

Finally, we can solve for x by multiplying both sides by -2:

x = (-2)*(-22.7) = 45.4

Therefore, the solution to the equation is x = 45.4.

Answer 3

We can translate this sentence into an equation:

"Half" means we will be multiplying by 1/2, or dividing by 2

"sum of x and 6.2" means to add x and 6.2, which would be x + 6.2

So "Half of the sum of x and 6.2" can be rewritten as 1/2(x + 6.2)

"the same as" means equals, =

"19.6 less than x" means to subtract 19.6 from x, or x-19.6

Putting this all together gives us an equation of:

1/2(x + 6.2) = x - 19.6

To solve this equation we can multiply both sides by 2. This will get rid of the fraction on the left side.

2*(1/2)(x + 6.2) = (x - 19.6)2

x + 6.2 = (x - 19.6)2

We can distribute the 2 to each term in the parenthesis on the right side.

x + 6.2 = 2x - 39.2

Next, we can combine our x's by subtracting an x from both sides. This cancels the x on the left side.

x - x + 6.2 = 2x - x - 39.2

6.2 = x - 39.2

Lastly, we can get x by itself by adding 39.2 to both sides.

6.2 + 39.2 = x - 39.2 + 39.2

45.4 = x