Solve for X 3

$3x+1=-2x+7$ (We wish to isolate $x$ in the left side of the equation, so we add $-2x$ to both sides of the equation.)

$3x+2x+1=-2x+2x+7$

$5x+1=7$ (Subtract $1$ from both sides of the equation.)

$5x+1-1=7-1$

$5x=6$ (Now divide both sides of the equation by $5$ to isolate $x$ )

$\dfrac{5x}{5}=\dfrac{6}{5}$

$\boxed{x=\dfrac{6}{5}}$

$\begin{aligned} 3x + 1 & = -2x + 7\\ 5x & = 6\\ x & = \color{#3D99F6}{\boxed{\dfrac{6}{5}}} \end{aligned}$

Here are the steps to solve this equation for $x$ .

$3x + 1 = -2x + 7$

$3x + 1 -1 = -2x + 7 - 1$

$3x = -2x + 6$

$3x + 2x = -2x + 6 + 2x$

$5x = 6$

$\frac{5x}{5} = \frac{6}{5}$

$x = \frac{6}{5}$

What does it mean to isolate the variable

Solving gives: $\begin{aligned} 3x + 1 &= -2x + 7 \\ 3x + 2x &= 7 - 1 \\ 5x &= 6 \\ x &= \boxed{\frac{6}{5}} \end{aligned}$ Therefore, the answer is $\displaystyle \frac{6}{5}$ .