Simplify the Expression: 31x+5z-(34x-(-13z))

We begin by addressing the innermost parentheses:

Remember that:

When we multiply a negative number by a negative number, the result will be positive.

Thus we obtain:

$31x+5z-(34x+13z)=$

Next we address the exercise within the parentheses:

Remember that:

When we multiply a positive number by a negative number, the result will be negative.

$31x+5z-34x-13z=$

We join the x coefficients:

$31x-34x=-3x$

We join the z coefficients:

$5z-13x=-8z$

We obtain the following:

$-3x-8z$