A) What is the value of x in the equation 4(2x+1)=27+3(2x−5)4(2x+1)=27+3(2x−5)? (1 point) Responses x = 7.5 x = 7.5 x = 4 x = 4 x = 9 x = 9 x = 21 x = 21

Answer 1

To solve the equation $4(2x+1)=27+3(2x-5)$, we can follow these steps:

1. Distribute both sides: $$4(2x)+4(1)=27+3(2x)-3(5)$$ Which simplifies to: $$8x+4=27+6x-15$$

2. Combine like terms on the right side: $$27-15=12\Rightarrow 8x+4=6x+12$$

3. Isolate $x$:

   • Subtract $6x$ from both sides: $$8x-6x+4=12$$ $$2x+4=12$$
   • Subtract $4$ from both sides: $$2x=8$$
   • Divide by $2$: $$x=4$$

Thus, the value of $x$ is 4.