Math

Question Solve the equation πx+3=4πx\pi x + 3 = 4\pi x for xx.

Studdy Solution

STEP 1

Assumptions
1. The equation to solve is πx+3=4πx\pi x + 3 = 4 \pi x.
2. We will solve for xx.

STEP 2

First, we need to isolate the variable xx on one side of the equation. We can do this by subtracting πx\pi x from both sides of the equation.
πx+3πx=4πxπx\pi x + 3 - \pi x = 4 \pi x - \pi x

STEP 3

Simplify both sides of the equation by combining like terms.
3=3πx3 = 3 \pi x

STEP 4

Now, to solve for xx, we need to divide both sides of the equation by 3π3 \pi.
33π=3πx3π\frac{3}{3 \pi} = \frac{3 \pi x}{3 \pi}

STEP 5

Simplify the equation by canceling out the common factors.
33π=x\frac{3}{3 \pi} = x

STEP 6

Further simplify the fraction by dividing 3 by 3.
1π=x\frac{1}{\pi} = x

STEP 7

Thus, the solution for xx is:
x=1πx = \frac{1}{\pi}

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