Question

10
select the expressions that are equivalent to $-42(-3x - 5)$.
$\square$ $-4(-6x - 5)$
$\square$ $-4(-6x - 10)$
$\square$ $24x - 40$
$\square$ $-8(12x + 20)$
$\square$ $8(3x + 5)$

Explanation:

Step1: Simplify the inner parentheses

First, simplify the expression inside the brackets: \(2(-3x - 5)\). Using the distributive property \(a(b + c)=ab+ac\), we have \(2\times(-3x)+2\times(-5)= -6x - 10\). So the original expression becomes \(-4(-6x - 10)\). So the second option \(-4(-6x - 10)\) is equivalent.

Step2: Simplify the entire expression

Now, simplify \(-4(-6x - 10)\) using the distributive property. \(-4\times(-6x)+(-4)\times(-10)=24x + 40\)? Wait, no, wait, let's do it again. Wait, \(-4\times(-6x)=24x\) and \(-4\times(-10) = 40\), so \(24x + 40\)? Wait, but let's check the fifth option: \(8(3x + 5)\). Let's expand \(8(3x + 5)=24x+40\), which is the same as \(-4\times2\times(-3x - 5)= -8\times(-3x - 5)=24x + 40\), and \(8(3x + 5)=24x + 40\). Also, let's check the second option: \(-4(-6x - 10)=24x + 40\) (since \(-4\times(-6x)=24x\) and \(-4\times(-10)=40\)). Wait, earlier when I simplified \(2(-3x -5)\) I got \(-6x -10\), so \(-4(-6x -10)\) is correct. Let's re - check the original expression: \(-4[2(-3x -5)]=-4\times( - 6x-10)=24x + 40\). Now let's check each option:

• First option: \(-4(-6x -5)=24x + 20

eq24x + 40\), so not equivalent.

• Second option: \(-4(-6x -10)=24x + 40\), equivalent.
• Third option: \(24x-40

eq24x + 40\), not equivalent.

• Fourth option: \(-8(12x + 20)=-96x-160

eq24x + 40\), not equivalent.

• Fifth option: \(8(3x + 5)=24x + 40\), equivalent.

Answer:

B. \(-4(-6x - 10)\), E. \(8(3x + 5)\)