What is (2(4p+1))/5 <= (3+12p)/4 ?

The solution to (2(4p+1))/5 =-1/4

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(2(4p+1))/5 <= (3+12p)/4

\frac{2 ( 4 p + 1 )}{5} \leq \frac{3 + 12 p}{4}

p \geq - \frac{1}{4}

Solution steps

\frac{2 ( 4 p + 1 )}{5} \leq \frac{3 + 12 p}{4}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

2 (4 p + 1) \cdot 4 \leq 5 (3 + 12 p)

Simplify

8 (4 p + 1) \leq 5 (3 + 12 p)

Expand

8 (4 p + 1) : 32 p + 8

Expand

5 (3 + 12 p) : 15 + 60 p

32 p + 8 \leq 15 + 60 p

Move

8

to the right side

32 p \leq 60 p + 7

Move

60 p

to the left side

- 28 p \leq 7

Multiply both sides by

- 1

28 p \geq - 7

Divide both sides by

28

p \geq - \frac{1}{4}

224 a z + 56 a c - 84 yz - 21 yc

\frac{- 6 + 8 i}{- 4 - 3 i}

\frac{8 + 5 i}{3 - 2 i}

9 \leq 4 x - 11 \leq 21

8 1^{\frac{3}{4}}

What is (2(4p+1))/5 <= (3+12p)/4 ?
The solution to (2(4p+1))/5 <= (3+12p)/4 is p>=-1/4