Question

for each inequality, choose the statement that describes its solution. if applicable, give the solution. (a) $4(7v + 5) > 28v + 20$ \bigcirc no solution \bigcirc $v < \square$ \bigcirc $v > \square$ \bigcirc all real numbers are solutions (b) $-3(u + 5) + 31 \leq 3(4 - u)$ \bigcirc no solution \bigcirc $u \leq \square$ \bigcirc $u \geq \square$ \bigcirc all real numbers are solutions

Explanation:

Step1: Expand left side of (a)

$4(7v+5)=28v+20$

Step2: Simplify inequality (a)

$28v+20>28v+20$
Subtract $28v+20$ from both sides: $0>0$, which is false.

Step3: Expand both sides of (b)

Left: $-3(u+5)+31=-3u-15+31=-3u+16$
Right: $3(4-u)=12-3u$

Step4: Simplify inequality (b)

$-3u+16\leq12-3u$
Add $3u$ to both sides: $16\leq12$, which is false.

Answer:

(a) No solution
(b) No solution