Question

real numbers
identifying equivalent algebraic expressions
for each expression, select all equivalent expressions from the list.
(a) $6(9x - 5)$
$\square$ $15x - 5$
$\square$ $54x - 30$
$\square$ $54x - 5$
$\square$ $6\cdot 9x - 6\cdot 5$
(b) $7y + 3y + 4y$
$\square$ $14y$
$\square$ $7y - 7y$
$\square$ $7y + 7y$
$\square$ $14 + y$

Explanation:

Step1: Analyze part (a)

We start with the expression \( 6(9x - 5) \). Using the distributive property \( a(b - c)=ab - ac \), we multiply 6 with each term inside the parentheses.
So, \( 6\times9x=54x \) and \( 6\times5 = 30 \). Thus, \( 6(9x - 5)=54x-30 \).

Step2: Analyze part (b)

We start with the expression \( 7y+3y + 4y \). First, combine like terms. \( 7y+3y=10y \), then \( 10y + 4y=14y \). Also, let's check other options:

• \( 7y - 7y=0

eq14y \)

• \( 7y + 2y=9y

eq14y \)

• \( 14 + y\) is not like terms with \( y \) terms. But \( 7y+3y + 4y=(7 + 3+4)y=14y \)

Answer:

(a) The equivalent expression for \( 6(9x - 5) \) is \( 54x - 30 \) (the third option in the first column).
(b) The equivalent expression for \( 7y+3y + 4y \) is \( 14y \) (the first option in the second column).