Question

Solve the inequality 0.08x + 0.1 and write the solution using: Interval Notation: Graph the solution below:

Answer 1

Given the inequality:

`0.08x+1.1\ge0.04x+0.1`

To solve the inequality,

step 1: Subtract 0.04x from both sides of the inequality.

Thus, we have

`\begin{gathered} 0.08x-0.04x+1.1\ge0.04x-0.04x+0.1 \\ \Rightarrow0.04x+1.1\ge0.1 \end{gathered}`

step 2: Subtract 1.1 from both sides of the inequality.

Thus, we have

`\begin{gathered} 0.04x+1.1-1.1\ge0.1-1.1 \\ \Rightarrow0.04x\ge-1 \end{gathered}`

step 3: Divide both sides of the inequality by the coefficient of x.

The coefficient of x is 0.04.

Thus, we have

`\begin{gathered} (0.04x)/(0.04)\ge(-1)/(0.04) \\ \Rightarrow x\ge-25 \end{gathered}`

Hence, in interval notation, we have

`\:[-25,\:\infty \:)`

The graph of the solution is thus: