Question

Can someone help me with my practice? I have a question I am unable to answer.

Answer 1

The inequality is:

`\left|2x-5\right|\leq5`

So, we have two options:

`\begin{gathered} 2x-5\leq5 \\ or \\ -(2x-5)\leq5 \end{gathered}`

Therefore solving both options, we get:

`\begin{gathered} 2x-5\leq5 \\ 2x-5+5\leq5+5 \\ 2x\leq10 \\ (2x)/(2)\leq(10)/(2) \\ x\leq5 \end{gathered}`
`\begin{gathered} -(2x-5)\leq5 \\ -2x+5\leq5 \\ -2x+5-5\leq5-5 \\ -2x\leq0 \\ (-2x)/(-2)\ge(0)/(-2) \\ x\ge0 \end{gathered}`

So, the answer is the set of all the x greater or equal to zero and smaller or equal to 5.

Answer: 0 ≤ x ≤ 5