Question

(a) select all equivalent expressions from the list for the expression.
$x + x + x + x + x$
$\square\\ 5 + x$ $\square\\ 5x$ $\square\\ 3x - 2x$ $\square\\ x + 5$

(b) select all equivalent expressions from the list for the expression.
$28y - 8$
$\square\\ 4(7y - 2)$ $\square\\ 20y$ $\square\\ 14y - 4$ $\square\\ 4 \cdot 7y - 4 \cdot 2$

Explanation:

Step1: Simplify the base expression (a)

$x+x+x+x+x = 5x$

Step2: Match with options (a)

• $5+x$: Not equal to $5x$
• $5x$: Equal to the simplified expression
• $3x-2x = x$: Not equal to $5x$
• $x+5$: Not equal to $5x$

Step3: Simplify the base expression (b)

$28y-8$

Step4: Verify each option (b)

• $4(7y-2) = 28y-8$: Equal to the base expression
• $20y$: Not equal to $28y-8$
• $14y-4$: Not equal to $28y-8$
• $4\cdot7y - 4\cdot2 = 28y-8$: Equal to the base expression

Answer:

(a) 5x
(b) 4(7y-2), $4\cdot7y - 4\cdot2$