Question

for each inequality, choose the statement that describes its solution. if applicable, give the solution. (a) $-2(u + 5)+26\geq2(6 - u)$ \bigcirc no solution \bigcirc $u\leq\square$ \bigcirc $u\geq\square$ \bigcirc all real numbers are solutions (b) $5(4 - w)+5w\lt20$ \bigcirc no solution \bigcirc $w\lt\square$ \bigcirc $w\gt\square$ \bigcirc all real numbers are solutions

Explanation:

Step1: Expand both sides of (a)

$-2u - 10 + 26 \geq 12 - 2u$

Step2: Simplify both sides of (a)

$-2u + 16 \geq 12 - 2u$

Step3: Isolate terms with $u$ (a)

$-2u + 2u \geq 12 - 16$

Step4: Simplify to check validity (a)

$0 \geq -4$

Step5: Expand both sides of (b)

$20 - 5w + 5w < 20$

Step6: Simplify both sides of (b)

$20 < 20$

Answer:

(a) All real numbers are solutions
(b) No solution