Question

Solve the inequalities. State whether the inequalities have no solutions or real solutions.2( 3d - 4) < 4 + 6d -15

Answer 1

The inequality is given to be:

`2(3d-4)<4+6d-15`

Step 1: Simplify the right-hand side of the inequality

`2(3d-4)<6d-11`

Step 2: Expand the bracket on the left-hand side of the inequality

`6d-8<6d-11`

Step 3: Add 8 to both sides of the inequality

`\begin{gathered} 6d-8+8<6d-11+8 \\ 6d<6d-3 \end{gathered}`

Step 4: Subtract 6d from both sides of the inequality

`\begin{gathered} 6d-6d<6d-3-6d \\ 0<-3 \end{gathered}`

Since we know that 0 is actually greater than -3, it means that the statement above is untrue.

Therefore, the inequality has NO SOLUTION.