What is -(x+5)/2 <= (12+3x)/4 ?

The solution to -(x+5)/2 =-22/5

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-(x+5)/2 <= (12+3x)/4

- \frac{x + 5}{2} \leq \frac{12 + 3 x}{4}

x \geq - \frac{22}{5}

Interval Notation

[- \frac{22}{5}, \infty)

Decimal Notation

x \geq - 4.4

Solution steps

- \frac{x + 5}{2} \leq \frac{12 + 3 x}{4}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

- (x + 5) \cdot 4 \leq 2 (12 + 3 x)

Expand

- (x + 5) \cdot 4 : - 4 x - 20

Expand

2 (12 + 3 x) : 24 + 6 x

- 4 x - 20 \leq 24 + 6 x

Move

20

to the right side

- 4 x \leq 6 x + 44

Move

6 x

to the left side

- 10 x \leq 44

Multiply both sides by

- 1

10 x \geq - 44

Divide both sides by

10

x \geq - \frac{22}{5}

9 x^{2} - 6 x + 5 = 0

\frac{x ^{2} - 2}{1 - 2 x} > 1

\frac{x - 3}{x + 2} < 0

2 c + (3 c - 4) = 5 c - 4

3 n^{2} - 72 n + 432

What is -(x+5)/2 <= (12+3x)/4 ?
The solution to -(x+5)/2 <= (12+3x)/4 is x>=-22/5