Solve for x in the equation 102.5(x−11.92)=71.6 . Round your answer to 3 decimal places.(1 point) Responses 12.619 12.619 −11.221 negative 11.221 0.699 0.699 12.618
To solve the equation 102.5(x−11.92)=71.6 for x, you can follow these steps:
1. Distribute the 102.5 to both terms inside the parentheses:
102.5x - 102.5(11.92) = 71.6
2. Simplify the expression on the right side of the equation by calculating 102.5 times 11.92:
102.5x - 1219 = 71.6
3. Isolate the variable by moving the constant term (-1219) to the other side of the equation:
102.5x = 71.6 + 1219
4. Combine the like terms on the right side:
102.5x = 1290.6
5. Finally, divide both sides of the equation by 102.5 to solve for x:
x = 1290.6 / 102.5
Now, let's calculate the value of x:
x ≈ 12.619 (rounded to 3 decimal places)
Therefore, the correct answer is 12.619.
To solve for x, we can start by distributing 102.5 to the terms inside the parentheses:
102.5(x−11.92) = 71.6
102.5x - 102.5(11.92) = 71.6
102.5x - 1208.1 = 71.6
Next, we can isolate the variable x by adding 1208.1 to both sides of the equation:
102.5x - 1208.1 + 1208.1 = 71.6 + 1208.1
102.5x = 1279.7
Finally, we can solve for x by dividing both sides of the equation by 102.5:
x = 1279.7 / 102.5
x ≈ 12.484
Rounded to 3 decimal places, x ≈ 12.484. Thus, the correct answer is not listed among the choices provided.
To solve the equation, we will isolate the variable x.
First, distribute 102.5 to the terms inside the parentheses:
102.5(x - 11.92) = 71.6
102.5x - 102.5(11.92) = 71.6
102.5x - 1202.9 = 71.6
Next, let's move the constant term to the other side of the equation:
102.5x = 71.6 + 1202.9
102.5x = 1274.5
Finally, to solve for x, we will divide both sides of the equation by 102.5:
x = 1274.5 / 102.5
x ≈ 12.424
Rounding to 3 decimal places, x ≈ 12.424.
Therefore, the correct response is 12.424.