What is 1/2 (4x+2)> 1/3 (x+2) ?

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

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1/2 (4x+2)> 1/3 (x+2)

\frac{1}{2} (4 x + 2) > \frac{1}{3} (x + 2)

x > - \frac{1}{5}

Interval Notation

(- \frac{1}{5}, \infty)

Decimal Notation

x > - 0.2

Solution steps

\frac{1}{2} (4 x + 2) > \frac{1}{3} (x + 2)

Expand

\frac{1}{2} (4 x + 2) : 2 x + 1

Expand

\frac{1}{3} (x + 2) : \frac{1}{3} x + \frac{2}{3}

2 x + 1 > \frac{1}{3} x + \frac{2}{3}

Move

1

to the right side

2 x > - \frac{1}{3} + \frac{1}{3} x

Move

\frac{1}{3} x

to the left side

\frac{5}{3} x > - \frac{1}{3}

Multiply both sides by

3

5 x > - 1

Divide both sides by

5

x > - \frac{1}{5}

6 x^{2} - 5 x - 14

x^{2} - 13 x + 36

- 6 x + \frac{1}{3} = - 16

- \frac{23}{2} (\frac{1}{100}) + \frac{23}{2}

- 2 = g - 9