Question

select the two expressions that are equivalent to -4.5 - 2(3x - 4). the options are: 3.5 - 6x, 26 - 19.5x, -12.5 - 6x, -4.5 - 6x - 8, -4.5 - 6x + 8

Explanation:

Step1: Distribute the -2

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = - 2\), \(b=3x\) and \(c=-4\). So, \(-2(3x - 4)=-2\times3x-2\times(-4)=-6x + 8\). The original expression \(-4.5-2(3x - 4)\) becomes \(-4.5-6x + 8\).

Step2: Combine like terms

Combine the constant terms \(-4.5\) and \(8\). \(-4.5 + 8=3.5\). So the expression simplifies to \(3.5-6x\).

Now we check the given options:

• Option \(3.5 - 6x\): Matches our simplified form.
• Option \(-4.5-6x + 8\): Matches the form after distributing the \(-2\) (Step 1).
• Other options:
• \(26-19.5x\): No relation to our simplified expression.
• \(-12.5 - 6x\): \(-4.5-8=-12.5\) but we have \(-4.5 + 8\), so this is incorrect.
• \(-4.5-6x - 8\): We have \(-2\times(-4) = + 8\) not \(-8\), so this is incorrect.

Answer:

\(3.5 - 6x\), \(-4.5 - 6x + 8\)