To solve an equation, the two main steps are:

isolate the variable term by moving the variables to one side and the constants to the other isolate the variable by multiplying or dividing both sides by the coefficient of the variable term, if necessary

Before we can isolate the variable term in \(\displaystyle{x}+{\left(\frac{{3}}{{2}}\right)}+{x}+{\left(\frac{{2}}{{3}}\right)}=−{\left(−{x}−{2}\right)}\), we need to simplify both sides of the equation.

Combining the like terms on the left side of the equation gives \(\displaystyle{2}{x}+{\left(\frac{{13}}{{6}}\right)}=−{\left(−{x}−{2}\right)}\).

Distributing the negative on the right side of the equation gives \(\displaystyle{2}{x}+{\left(\frac{{13}}{{6}}\right)}={x}+{2}\).

Now that both sides are simplified, we can move the variable terms to one side and the constants to the other.

Subtracting xx on both sides gives \(\displaystyle{x}+{\left(\frac{{13}}{{6}}\right)}={2}\).

Subtracting 13/6 on both sides gives \(\displaystyle{x}=−{\left(\frac{{1}}{{6}}\right)}\).

The solution of the equation is then \(\displaystyle{x}=−{\left(\frac{{1}}{{6}}\right)}\).

isolate the variable term by moving the variables to one side and the constants to the other isolate the variable by multiplying or dividing both sides by the coefficient of the variable term, if necessary

Before we can isolate the variable term in \(\displaystyle{x}+{\left(\frac{{3}}{{2}}\right)}+{x}+{\left(\frac{{2}}{{3}}\right)}=−{\left(−{x}−{2}\right)}\), we need to simplify both sides of the equation.

Combining the like terms on the left side of the equation gives \(\displaystyle{2}{x}+{\left(\frac{{13}}{{6}}\right)}=−{\left(−{x}−{2}\right)}\).

Distributing the negative on the right side of the equation gives \(\displaystyle{2}{x}+{\left(\frac{{13}}{{6}}\right)}={x}+{2}\).

Now that both sides are simplified, we can move the variable terms to one side and the constants to the other.

Subtracting xx on both sides gives \(\displaystyle{x}+{\left(\frac{{13}}{{6}}\right)}={2}\).

Subtracting 13/6 on both sides gives \(\displaystyle{x}=−{\left(\frac{{1}}{{6}}\right)}\).

The solution of the equation is then \(\displaystyle{x}=−{\left(\frac{{1}}{{6}}\right)}\).