Question

solve: 10x + 3+3x = 5x + 1+2(4x + 1)
infinitely many solutions
x = 3
no solutions
x=-3

Explanation:

Step1: Expand the right - hand side

First, expand $2(4x + 1)$ using the distributive property $a(b + c)=ab+ac$. So $2(4x + 1)=8x+2$. The original equation $10x + 3+3x=5x + 1+2(4x + 1)$ becomes $10x + 3+3x=5x + 1+8x+2$.

Step2: Combine like terms on both sides

On the left - hand side, combine $10x$ and $3x$: $10x+3x = 13x$, so the left - hand side is $13x + 3$. On the right - hand side, combine $5x$ and $8x$ and $1$ and $2$: $5x+8x=13x$ and $1 + 2=3$, so the right - hand side is $13x+3$.

Step3: Analyze the resulting equation

We have the equation $13x + 3=13x+3$. Subtract $13x$ from both sides: $(13x - 13x)+3=(13x - 13x)+3$, which simplifies to $3 = 3$. This is a true statement for all values of $x$.

Answer:

infinitely many solutions