Question

solve.

use the distributive property to write an expression that is equivalent to ( 12x - 4 ).

use the distributive property to write an expression that is equivalent to ( 12 - 15x ).

use the distributive property to write an expression that is equivalent to ( 42x + 12 ).

evaluate ( 42x + 12 ) and the equivalent expression that you wrote in problem 7 for ( x = 2 ). what do you notice about the value of the two expressions?
show your work.
solution:

four students were asked to write an expression that is equivalent to ( 4x - 16 ). the students’ responses and the expressions they wrote are shown in the table.

student	expression
javed	( 4(2x - 12) )
suga	( -4(-4x + 16) )
ilsa	( 2(6x - 10) )

a. which student(s) wrote correct expressions?

b. for each incorrect expression, explain what the student did to get his or her answer.

Explanation:

Step1: Factor out 5 from $15x-45$

$5(3x - 9)$

Step2: Factor out -3 from $12-15x$

$-3(5x - 4)$

Step3: Factor out 6 from $42x+12$

$6(7x + 2)$

Step4: Evaluate $42x+12$ at $x=2$

$42(2)+12=84+12=96$

Step5: Evaluate $6(7x+2)$ at $x=2$

$6(7(2)+2)=6(14+2)=6(16)=96$

Step6: Check equivalence for $4x-20$

• Ali: $-4(5 - x)=-20+4x=4x-20$ (correct)
• Ling: $4(2x - 5)=8x-20$ (incorrect, wrong coefficient)
• Juan: $-4(-x + 5)=4x-20$ (correct)
• Lila: $2(2x - 10)=4x-20$ (correct)

Answer:

1. $5(3x - 9)$
2. $-3(5x - 4)$
3. $6(7x + 2)$
4. Both expressions equal 96; they are equivalent.

5a. Ali, Juan, and Lila wrote correct expressions.
5b.

• Ali: Factored out -4 from $4x-20$ as $-4(5 - x)$, which expands back to $4x-20$.
• Ling: Incorrectly used 2x instead of x inside the parentheses, so $4(2x-5)$ expands to $8x-20$, not $4x-20$.
• Juan: Factored out -4 from $4x-20$ as $-4(-x + 5)$, which expands back to $4x-20$.
• Lila: Factored out 2 from $4x-20$ as $2(2x - 10)$, which expands back to $4x-20$.