Question

solve for ( x ):
( 5x - 4 geq 12 ) and ( 12x + 5 leq -4 )
choose 1 answer:
a ( x geq \frac{16}{5} ) or ( x leq -\frac{3}{4} )
b ( x leq \frac{16}{5} )
c ( x geq -\frac{3}{4} )
d there are no solutions
e all values of ( x ) are solutions

Explanation:

Step1: Solve \( 5x - 4 \geq 12 \)

Add 4 to both sides: \( 5x - 4 + 4 \geq 12 + 4 \)
Simplify: \( 5x \geq 16 \)
Divide by 5: \( x \geq \frac{16}{5} \)

Step2: Solve \( 12x + 5 \leq -4 \)

Subtract 5 from both sides: \( 12x + 5 - 5 \leq -4 - 5 \)
Simplify: \( 12x \leq -9 \)
Divide by 12: \( x \leq \frac{-9}{12} = -\frac{3}{4} \)

Step3: Analyze the "AND" condition

We need \( x \geq \frac{16}{5} \) AND \( x \leq -\frac{3}{4} \). But \( \frac{16}{5}=3.2 \) and \( -\frac{3}{4}=-0.75 \), a number can't be both ≥ 3.2 and ≤ -0.75. So no solutions.

Answer:

D. There are no solutions