What is ((4x+2))/3 <= ((25-2x))/4 ?

The solution to ((4x+2))/3 <= ((25-2x))/4 is x<= 67/22

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((4x+2))/3 <= ((25-2x))/4

\frac{( 4 x + 2 )}{3} \leq \frac{( 25 - 2 x )}{4}

x \leq \frac{67}{22}

Interval Notation

(- \infty, \frac{67}{22}]

Decimal Notation

x \leq 3.04545 \dots

Solution steps

\frac{( 4 x + 2 )}{3} \leq \frac{( 25 - 2 x )}{4}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

(4 x + 2) \cdot 4 \leq 3 (25 - 2 x)

Expand

(4 x + 2) \cdot 4 : 16 x + 8

Expand

3 (25 - 2 x) : 75 - 6 x

16 x + 8 \leq 75 - 6 x

Move

8

to the right side

16 x \leq - 6 x + 67

Move

6 x

to the left side

22 x \leq 67

Divide both sides by

22

x \leq \frac{67}{22}

4 (x + 7) > 3 (x + 2)

5 - 2 x \leq 3

∣ 2 ∣ \cdot x ∣ - 3 ∣ < 1

\frac{x - 4}{5} > \frac{1}{5}

- 5 a \geq 0

What is ((4x+2))/3 <= ((25-2x))/4 ?
The solution to ((4x+2))/3 <= ((25-2x))/4 is x<= 67/22