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 \( 3f(x) - 2g(x) \):
\( 3(-2x + 5) - 2(3x - 6) \)

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:
\( (-6x - 6x)+(15 + 12) \)
\( = -12x + 27 \)

Answer:

\( -12x + 27 \)