Which expressions are equivalent? Select two answers.
A. 2 (x+3) + 2x and 4x + 3
B. -2+4 (x +3) and 4x + 10
C 3 +5 (x 1) and 8x – 5
D. 5x – 2 (x + 4) and 3x + 8
E 4-5 (x + 2) and 5x – 6
C and A
What's the rest of the quiz
Yeah what's the rest of the quiz for oca
Only B.
- 2 + 4 ( x + 3 ) = - 2 + 4 ∙ x + 4 ∙ 3 = 4 x + 12 - 2 = 4 x + 10
A AND D
Well, let me put on my clown nose and think about this one.
Hmm, it looks like options A and E are the odd ones out here. Option A is equivalent to 4x + 3, not 4x + 6. And option E is equivalent to -5x + 4, not 5x - 6.
So, the two expressions that are equivalent are B. -2 + 4(x + 3) and 4x + 10, and C. 3 + 5(x - 1) and 8x - 5. They both hold true and are equivalent.
To determine which expressions are equivalent, we need to simplify each expression and see if they result in the same final expression.
Let's go through each option:
A. 2(x+3) + 2x can be simplified by distributing the 2 to both terms inside the parentheses:
= 2x + 6 + 2x
= 4x + 6
This expression is NOT equivalent to 4x + 3.
B. -2 + 4(x + 3) can be simplified by distributing the 4 to both terms inside the parentheses:
= -2 + 4x + 12
= 4x + 10
This expression IS equivalent to 4x + 10.
C. 3 + 5(x - 1) can be simplified by distributing the 5 to both terms inside the parentheses:
= 3 + 5x - 5
= 5x - 2
This expression is NOT equivalent to 8x - 5.
D. 5x - 2(x + 4) can be simplified by distributing the -2 to both terms inside the parentheses:
= 5x - 2x - 8
= 3x - 8
This expression IS equivalent to 3x + 8.
E. 4 - 5(x + 2) can be simplified by distributing the -5 to both terms inside the parentheses:
= 4 - 5x - 10
= -5x - 6
This expression is NOT equivalent to 5x - 6.
So, the two equivalent expressions are:
B. -2 + 4(x + 3) and 4x + 10
D. 5x - 2(x + 4) and 3x + 8