Question

is $1 + 4(3x - 10) - 12x$ equivalent to $-39$? explain.

Explanation:

Step1: Expand the expression

First, we expand \(4(3x - 10)\) using the distributive property \(a(b - c)=ab - ac\). So, \(4(3x - 10)=4\times3x-4\times10 = 12x - 40\).
The original expression \(1 + 4(3x - 10)-12x\) becomes \(1+(12x - 40)-12x\).

Step2: Combine like terms

Now, we combine the like terms. First, remove the parentheses: \(1 + 12x - 40 - 12x\).
Then, combine the \(x\)-terms: \(12x - 12x = 0\).
Next, combine the constant terms: \(1 - 40=-39\).

Answer:

Yes, \(1 + 4(3x - 10)-12x\) is equivalent to \(-39\) because when we expand and combine like terms in the expression \(1 + 4(3x - 10)-12x\), we get \(-39\).