Question

Solve the compound inequality 4x-4< 12 and 3x+ 5 < 8

Answer 1

We have the compound inequality in one variable: 4x - 4 < 12 and 3x+ 5 < 8.

We can solve them individually and then and see which are the limits for x.

We start with 4x - 4 < 12:

`\begin{gathered} 4x-4<12 \\ 4x<12+4 \\ 4x<16 \\ x<(16)/(4) \\ x<4 \end{gathered}`

Then, we continue with 3x + 5 < 8:

`\begin{gathered} 3x+5<8 \\ 3x<8-5 \\ 3x<3 \\ x<1 \end{gathered}`

If we combine the two inequalities, we can see that there is no minimum limit for x, but we have two upper limits for x: x < 4 and x < 1.

The last includes the former, as all values that satisfy x < 1 also satisfy x < 4.

Then, the solution interval for this inequality is x < 1.

Answer: x < 1