Solve the following linear equation for x. 5x-2+x=9+3x+10 x=

To solve the linear equation $5x - 2 + x = 9 + 3x + 10$, we can start by simplifying both sides of the equation.<br /><br />On the left side, we can combine like terms:<br />$5x - 2 + x = 6x - 2$<br /><br />On the right side, we can combine like terms:<br />$9 + 3x + 10 = 3x + 19$<br /><br />Now, we can set the simplified expressions equal to each other:<br />$6x - 2 = 3x + 19$<br /><br />Next, we can isolate the variable $x$ by subtracting $3x$ from both sides:<br />$6x - 3x - 2 = 19$<br /><br />Simplifying further, we have:<br />$3x - 2 = 19$<br /><br />To isolate $x$, we can add $2$ to both sides:<br />$3x - 2 + 2 = 19 + 2$<br /><br />Simplifying further, we have:<br />$3x = 21$<br /><br />Finally, we can divide both sides by $3$ to solve for $x$:<br />$\frac{3x}{3} = \frac{21}{3}$<br /><br />Simplifying further, we have:<br />$x = 7$<br /><br />Therefore, the solution to the linear equation is $x = 7$.