Question

Solve the inequalities. State whether the inequalities have no solutions or real solutions.4( 3 - 2x) > 2( 6 - 4x)

Answer 1

Given an inequalities show if it have no solutions or real solutions:

`4(3-2x)>2(6-4x)`

Step 1: Expand the inequalities

`\begin{gathered} 4(3-2x)>2(6-4x) \\ 12-8x>12-8x \end{gathered}`

Step 2: Subtract 12 from both side of the inequalities

`\begin{gathered} 12-8x>12-8x \\ \text{subtract 12 from both side} \\ 12-8x-12>12-8x-12 \\ -8x>-8x \end{gathered}`

Step 3: Add 8x to both side of the inequalities

`\begin{gathered} -8x>-8x \\ \text{add 8x to both side} \\ -8x+8x>-8x+8x \\ 0>0 \end{gathered}`

Therefore the solution for the above inequalities is No solution