Question

(a) select all equivalent expressions from the list for the expression. 3x + 15 □ 3·x + 3·5 □ 3(x + 5) □ 3(5x + 1) □ 18x (b) select all equivalent expressions from the list for the expression. 10 + 11y - 1 - y □ 10 + 9y □ 9y + 10y □ 9y + 10 □ 10y + 9

Explanation:

(a) Step1: Rewrite original expression

$3x + 15 = 3\cdot x + 3\cdot5$

(a) Step2: Factor out common term

$3\cdot x + 3\cdot5 = 3(x+5)$

(a) Step3: Eliminate non-equivalent options

$3(5x+1)=15x+3
eq3x+15$, $18x
eq3x+15$

(b) Step1: Combine constant terms

$10-1=9$

(b) Step2: Combine variable terms

$11y - y = 10y$

(b) Step3: Form simplified expression

$10y + 9$

(b) Step4: Eliminate non-equivalent options

$10+9y
eq10y+9$, $9y+10y=19y
eq10y+9$, $9y+10
eq10y+9$

Answer:

(a) 3⋅x + 3⋅5, 3(x+5)
(b) 10y + 9