Question

1. write an equivalent expression to $3f(x) - 2g(x)$, if $f(x) = -2x + 5$ and $g(x) = 3x - 6$.

Explanation:

Step1: Substitute f(x) and g(x)

Substitute \( f(x) = -2x + 5 \) and \( g(x) = 3x - 6 \) into \( 3f(x) - 2g(x) \), we get:
\( 3(-2x + 5) - 2(3x - 6) \)

Step2: Distribute the coefficients

Distribute 3 and -2:
\( 3\times(-2x) + 3\times5 - 2\times3x + (-2)\times(-6) \)
\( = -6x + 15 - 6x + 12 \)

Step3: Combine like terms

Combine the x - terms and the constant terms:
For x - terms: \( -6x - 6x=-12x \)
For constant terms: \( 15 + 12 = 27 \)
So the expression becomes \( -12x + 27 \)

Answer:

\(-12x + 27\) (The boxes would be filled as -12, +, 27 respectively)