Question

1. what is the simplified expression equivalent to $3m - 4n$, when $m = 5x - 2$ and $n = 4 - 3x$?

Explanation:

Step1: Substitute M and N into the expression

We know that \( M = 5x - 2 \) and \( N = 4 - 3x \). Substitute these into \( 3M - 4N \):
\( 3(5x - 2) - 4(4 - 3x) \)

Step2: Distribute the coefficients

For \( 3(5x - 2) \), we get \( 3\times5x - 3\times2 = 15x - 6 \).
For \( -4(4 - 3x) \), we get \( -4\times4 + (-4)\times(-3x) = -16 + 12x \).

Step3: Combine like terms

Now we have \( 15x - 6 - 16 + 12x \). Combine the \( x \)-terms and the constant terms:
\( (15x + 12x) + (-6 - 16) = 27x - 22 \)

Answer:

\( 27x - 22 \)