Question

If f(x)= 3x-2 and g(x)= 5x+7, find 2f(x) + g(x)?

Answer 1

`11x+3`

Explanation:

setting up:

`\color(steelblue)(f(x)=3x-2)` and `\color(indianred)(g(x)=5x+7)`

therefore `2\color(steelblue)(f(x))+\color(indianred)(g(x))` becomes
`2[\color(steelblue)(3x-2)]+[\color(indianred)(5x+7)]`

solving:

`\color(seagreen)(2(3x-2))+5x+7` distribute colored part
`\color(seagreen)(2(3x)+2(-2))+5x+7`
`\color(seagreen)(6x+(-4))+5x+7` simplify
`6x-4+5x+7`

`\color(olive)(6x)\color(teal)(-4)\color(olive)(+5x)\color(teal)(+7)` identify like terms
`\color(olive)(6x+5x)\color(teal)(-4+7)`
`\color(olive)(11x)\color(teal)(+3)` combine like terms

answer: `11x+3`