Answer:
The required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]24x>18(4x-6)-30[/tex]
We need to solve the above inequity of x.
Open the parentheses.
[tex]24x>18\times 4x-18\times 6-30[/tex]
[tex]24x>72x-108-30[/tex]
[tex]24x>72x-138[/tex]
Subtract 72x from both sides.
[tex]24x-72x>72x-138-72x\\-48x>-138[/tex]
Multiply both sides by -1 and reverse the inequality.
[tex]\left(-48x\right)\left(-1\right)<\left(-138\right)\left(-1\right)[/tex]
[tex]48x<138[/tex]
Divide both side by 48.
[tex]x<\frac{23}{8}[/tex]
Hence, the required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
