Question

Solve the compound inequality.2x-5 33 and 3x-12-19Graph the solution on the number line:

Answer 1

Consider the system of inequalities,

`\begin{gathered} 2x-5\leq3 \\ 3x-1\ge-19 \end{gathered}`

Simplify the first inequality as follows,

`\begin{gathered} 2x-5+5\leq3+5 \\ 2x\cdot(1)/(2)\leq8\cdot(1)/(2) \\ x\leq4 \end{gathered}`

So, the solution to this inequality will be the set of points including and lying on the left of point 4 on the number line.

Simplify the second inequality as follows,

`\begin{gathered} 3x-1+1\ge-19+1 \\ 3x\cdot(1)/(3)\ge-18\cdot(1)/(3) \\ x\ge-6 \end{gathered}`

So, the solution to this inequality will be the set of points including and lying on the right of point -6 on the number line.

The solution to the compound inequality will be the common solution of both the inequalities, that is, the set of real numbers ranging from -6 to 4.

The solution can be seen on the number line as follows,