Question

how do I solve 2x-1<4 and -5x-3>-3 and write the solution in interval notation if no solution type 0

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} 2x-1<4 \\ -5x-3>-3 \\ \\ \end{gathered}`

We will proceed to solve as shown below:

`\begin{gathered} 2x-1<4 \\ \text{Add ''1'' to both sides, we have:} \\ 2x-1+1<4+1\Rightarrow2x<5 \\ 2x<5 \\ \text{Divide both sides by 2, we have:} \\ x<(5)/(2) \\ \\ -5x-3>-3 \\ \text{Add ''5x'' to both sides, we have:} \\ -5x+5x-3>-3+5x \\ -3>-3+5x \\ \text{Add ''3'' to both sides, we have:} \\ -3+3>-3+3+5x \\ 0>5x \\ \text{Divide both sides by 5, we have:} \\ (0)/(5)>(5)/(5)x \\ 0>x \\ x<0 \end{gathered}`

The solution is given by the intersecting points of the 2 functions

`\begin{gathered} \\ \lbrack0,-\infty\rbrack \end{gathered}`