Question

Solve each of the given compound inequalities. Enter your answers using interval notation.x−2≤0 or 7x−5≥65 Solution: x−2≤0 and 7x−5≥65 Solution:

Answer 1

Ok, so

We want to solve the following compound inequalities.

$x-2\leq0\ldots or\ldots7x-5\ge65$

We're going to solve each inequality as follows:

The first inequality:

$\begin{gathered} x-2\leq0 \\ x\leq2 \end{gathered}$

The second one:

$\begin{gathered} 7x-5\ge65 \\ 7x\ge70 \\ x\ge10 \end{gathered}$

And finally, put these solutions in the number line:

The solution in interval notation will be:

(-inf,2]U[10,inf)