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) into the expression

We know that \( f(x) = -2x + 5 \) and \( g(x) = 3x - 6 \). Substitute these into \( 3f(x)-2g(x) \):
\( 3(-2x + 5)-2(3x - 6) \)

Step2: Distribute the coefficients

Use the distributive property \( a(b + c)=ab+ac \):
\( 3\times(-2x)+3\times5-2\times3x+(-2)\times(-6) \)
\( = -6x + 15 - 6x + 12 \)

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:

\( -12x + 27 \)