Math

Question Solve for xx in the equation x7=10.2\frac{x}{7} = 10.2. The simplified solution is x=x = \square.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation x7=10.2\frac{x}{7} = 10.2.
2. We need to solve for the variable xx.
3. The solution must be simplified.

STEP 2

To solve for xx, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 7.
7×x7=7×10.27 \times \frac{x}{7} = 7 \times 10.2

STEP 3

On the left side of the equation, the 7 in the numerator and the 7 in the denominator cancel each other out, leaving us with xx.
x=7×10.2x = 7 \times 10.2

STEP 4

Now, we multiply 7 by 10.2 to find the value of xx.
x=7×10.2x = 7 \times 10.2

STEP 5

Calculate the product.
x=71.4x = 71.4
The solution is x=71.4x=71.4.

STEP 6

To check the solution, we substitute x=71.4x=71.4 back into the original equation and see if the left side equals the right side.
71.47=10.2\frac{71.4}{7} = 10.2

STEP 7

Perform the division on the left side of the equation.
10.2=10.210.2 = 10.2

STEP 8

Since both sides of the equation are equal, our solution x=71.4x=71.4 is correct.
The solution is x=71.4x=71.4.

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