Question

QuestionSolve the compound inequality, and write the solution in interval notation: 2 (3x + 1) < 20 and 4 (x - 1) < 2.

Answer 1

step 1

solve 2(3x+1) <20

Multiply

6x+2<20

6x<20-2

6x<18

x<3

The solution of the inequality A is the interval (-infinite, 3)

step 2

solve 4(x-1)<2

Multiply

4x-4<2

4x<2+4

4x<6

x<6/4

x<1.5

The solution of the inequality B is the interval

(-infinite, 1.5)

step 3

Find the solution of the compound inequality

the solution is the intersection both solutions

`\begin{gathered} \left(-infinite,3\right)\cap\left(-infinite,1.5\right) \\ \end{gathered}`

the solution is the interval

(-infinite, 1.5)