Question

Can someone show me how to solve and graph the following?

Answer 1

Given the combined inequality as;

`2<4x+10\leq14`

Then, we can break the combined inequality to two separate inequalities as;

`\begin{gathered} 2<4x+10 \\ \text{and} \\ 4x+10\leq14 \end{gathered}`

From the first inequality, we have;

`\begin{gathered} 2<4x+10 \\ 2-10<4x \\ -8<4x \\ -(8)/(4)<(4x)/(4) \\ -2-2 \end{gathered}`

On a number line, the solution to the first inequality is;

The arrow shows that the numbers to the right side are greater than -2.

Also, from second inequality, we have;

`\begin{gathered} 4x+10\leq14 \\ 4x\leq14-10 \\ 4x\leq4 \\ (4x)/(4)\leq(4)/(4) \\ x\leq1 \end{gathered}`

The solution of the second inequality on the number line is;

The graph shows the numbers that are less than or equal to 1.

Hence, the combined solution of the given inequality is;

[tex]-2and its graph is;