What is x/2+x/2 >5-x/6 ?

The solution to x/2+x/2 >5-x/6 is x> 30/7

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x/2+x/2 >5-x/6

\frac{x}{2} + \frac{x}{2} > 5 - \frac{x}{6}

x > \frac{30}{7}

Interval Notation

(\frac{30}{7}, \infty)

Decimal Notation

x > 4.28571 \dots

Solution steps

\frac{x}{2} + \frac{x}{2} > 5 - \frac{x}{6}

Add similar elements:

\frac{x}{2} + \frac{x}{2} = 2 \cdot \frac{x}{2}

2 \cdot \frac{x}{2} > 5 - \frac{x}{6}

Multiply fractions:

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

\frac{x \cdot 2}{2} > 5 - \frac{x}{6}

Cancel the common factor:

2

x > 5 - \frac{x}{6}

Multiply both sides by

6

6 x > 30 - x

Move

x

to the left side

7 x > 30

Divide both sides by

7

x > \frac{30}{7}

13 - 3 x < 61

2 (x - 3) > 10

9 + 8 x > 25

3 x + 9 < 4 x - 5

4 (2 x + 3) < 4 (x - 2)