What is 1/3 (x+4)-5/6 (x-3)>= 1/2 x+1 ?

The solution to 1/3 (x+4)-5/6 (x-3)>= 1/2 x+1 is x<= 17/6

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1/3 (x+4)-5/6 (x-3)>= 1/2 x+1

\frac{1}{3} (x + 4) - \frac{5}{6} (x - 3) \geq \frac{1}{2} x + 1

x \leq \frac{17}{6}

Interval Notation

(- \infty, \frac{17}{6}]

Decimal Notation

x \leq 2.83333 \dots

Solution steps

\frac{1}{3} (x + 4) - \frac{5}{6} (x - 3) \geq \frac{1}{2} x + 1

Expand

\frac{1}{3} (x + 4) - \frac{5}{6} (x - 3) : - \frac{x}{2} + \frac{23}{6}

- \frac{x}{2} + \frac{23}{6} \geq \frac{1}{2} x + 1

Move

\frac{23}{6}

to the right side

- \frac{x}{2} \geq - \frac{17}{6} + \frac{1}{2} x

Move

\frac{1}{2} x

to the left side

- x \geq - \frac{17}{6}

Multiply both sides by

- 1

x \leq \frac{17}{6}

x^{2} - 5 x - 3 = 2 x - 5

- 19.6 (\frac{45}{196})^{2} + 9 (\frac{45}{196}) + 3

(x - \frac{1}{4})^{2} = \frac{9}{16}

(\frac{9}{4})^{\frac{5}{2}}

\frac{1}{3} + \frac{2}{5}

What is 1/3 (x+4)-5/6 (x-3)>= 1/2 x+1 ?
The solution to 1/3 (x+4)-5/6 (x-3)>= 1/2 x+1 is x<= 17/6