What is the answer to 5/(2sqrt(5x-1))= 5/9 ?

The answer to 5/(2sqrt(5x-1))= 5/9 is x= 17/4

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5/(2sqrt(5x-1))= 5/9

\frac{5}{2 5 x - 1} = \frac{5}{9}

x = \frac{17}{4}

Decimal Notation

x = 4.25

Solution steps

\frac{5}{2 5 x - 1} = \frac{5}{9}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

5 \cdot 9 = 2 5 x - 1 \cdot 5

Expand

2 5 x - 1 \cdot 5 : 10 5 x - 1

5 \cdot 9 = 10 5 x - 1

Switch sides

10 5 x - 1 = 5 \cdot 9

Multiply the numbers:

5 \cdot 9 = 45

10 5 x - 1 = 45

Divide both sides by

10

5 x - 1 = \frac{9}{2}

Square both sides:

5 x - 1 = \frac{81}{4}

5 x - 1 = \frac{81}{4}

Solve

5 x - 1 = \frac{81}{4} : x = \frac{17}{4}

x = \frac{17}{4}

Verify Solutions:

x = \frac{17}{4}

True

The solution is

x = \frac{17}{4}

x - 7 + 12 = 28

x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} - 4 = 0

x + 5 = x - 7

8 = 14 - 5 x

3 - 3 x - 3 + x = 2

What is the answer to 5/(2sqrt(5x-1))= 5/9 ?
The answer to 5/(2sqrt(5x-1))= 5/9 is x= 17/4
Solve for x: 5/(2sqrt(5x-1))= 5/9
The solution is x= 17/4