What is 1+(10x)/(11)-1/10 (x+11)>= x ?

The solution to 1+(10x)/(11)-1/10 (x+11)>= x is x<=-11/21

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1+(10x)/(11)-1/10 (x+11)>= x

1 + \frac{10 x}{11} - \frac{1}{10} (x + 11) \geq x

x \leq - \frac{11}{21}

Interval Notation

(- \infty, - \frac{11}{21}]

Decimal Notation

x \leq - 0.52380 \dots

Solution steps

1 + \frac{10 x}{11} - \frac{1}{10} (x + 11) \geq x

Move

1

to the right side

\frac{10 x}{11} - \frac{1}{10} (x + 11) \geq x - 1

Multiply by LCM

100 x - 11 (x + 11) \geq 110 x - 110

Expand

- 11 (x + 11) : - 11 x - 121

100 x - 11 x - 121 \geq 110 x - 110

Add similar elements:

100 x - 11 x = 89 x

89 x - 121 \geq 110 x - 110

Move

121

to the right side

89 x \geq 110 x + 11

Move

110 x

to the left side

- 21 x \geq 11

Multiply both sides by

- 1

21 x \leq - 11

Divide both sides by

21

x \leq - \frac{11}{21}

\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}

6 (v - 5) - 2 v = 2

(\frac{1}{2}) (\frac{1}{2})

1 0^{5 l o g_{10} (5)}

What is 1+(10x)/(11)-1/10 (x+11)>= x ?
The solution to 1+(10x)/(11)-1/10 (x+11)>= x is x<=-11/21