Question

for each inequality, choose the statement that describes its solution. if applicable, give the solution. (a) $2(5y + 7) > 10y + 18$ \bigcirc no solution \bigcirc $y < \square$ \bigcirc $y > \square$ \bigcirc all real numbers are solutions (b) $3(6 - w) + 5w \leq 26$ \bigcirc no solution \bigcirc $w \leq \square$ \bigcirc $w \geq \square$ \bigcirc all real numbers are solutions

Explanation:

Step1: Expand left side of (a)

$2(5y+7) = 10y + 14$

Step2: Simplify inequality (a)

$10y + 14 > 10y + 18$
Subtract $10y$ from both sides: $14 > 18$

Step3: Expand left side of (b)

$3(6-w)+5w = 18 - 3w + 5w = 18 + 2w$

Step4: Isolate variable in (b)

$18 + 2w \leq 26$
Subtract 18: $2w \leq 8$
Divide by 2: $w \leq 4$

Answer:

(a) No solution
(b) $w \leq 4$