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

The solution to (1-(x-3))/2 >= x/(2+5) is x<= 28/9

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

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

x \leq \frac{28}{9}

Interval Notation

(- \infty, \frac{28}{9}]

Decimal Notation

x \leq 3.11111 \dots

Solution steps

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

(1 - (x - 3)) (2 + 5) \geq 2 x

Simplify

7 (- x + 4) \geq 2 x

Expand

7 (- x + 4) : - 7 x + 28

- 7 x + 28 \geq 2 x

Move

28

to the right side

- 7 x \geq 2 x - 28

Move

2 x

to the left side

- 9 x \geq - 28

Multiply both sides by

- 1

9 x \leq 28

Divide both sides by

9

x \leq \frac{28}{9}

2 (x + 1) - 3 (x - 2) \leq x + 6

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

\frac{x}{3 - 2} < 7

4 x - \frac{2}{2} - x - \frac{6}{4} > x + \frac{7}{2} - 3

23 - 6 x < - 7

What is (1-(x-3))/2 >= x/(2+5) ?
The solution to (1-(x-3))/2 >= x/(2+5) is x<= 28/9