Question

How do you solve $3x - 10 = 5x + 8$?

Answer 1

Hint:In order to determine the value of variable$x$ in the above equation use the rules of transposing terms to transpose terms having $(x)$on the Left-hand side and constant value terms on the Right-Hand side of the equation. Solving like terms and dividing both sides of the equation with the coefficient of $x$will lead to your required result.

Complete step by step solution:
We are given a linear equation in one variable $3x - 10 = 5x + 8$.and we have to solve this equation for variable ($x$).
$ \Rightarrow 3x - 10 = 5x + 8$

Now combining like terms on both of the sides. Terms having $x$ will on the Left-Hand side of the equation and constant terms on the right-hand side .

Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term get reversed .In our case,$ - 10$ will become $ + 10$on RHS and $5x$ in LHS will become $ - 5x$ in LHS

After transposing terms our equation becomes
$
\Rightarrow 3x - 5x = 10 + 8 \\
\Rightarrow - 2x = 18 \\
$

Now dividing both sides by the number $ - 2$
\[
\Rightarrow \dfrac{{ - 2x}}{{ - 2}} = \dfrac{{18}}{{ - 2}} \\
\Rightarrow x = - 9 \\
\]
Therefore, the solution to the equation $3x - 10 = 5x + 8$is equal to \[x = - 9\].

Note:Linear Equation: A linear equation is a equation which can be represented in the form of $ax + c$where $x$is the unknown variable and a,c are the numbers known where $a \ne 0$.If $a = 0$then the equation will become a constant value and will no longer be a linear equation .