Answer: x<4
Given the inequality:
[tex]10x>2(8x-3)-18[/tex]We want to solve the inequality for x.
First, distribute the bracket on the right side of the inequality.
[tex]\begin{gathered} 10x>2(8x)-2(3)-18 \\ 10x>16x-6-18 \\ 10x>16x-24 \end{gathered}[/tex]Next, subtract 10x from both sides of the inequality.
[tex]\begin{gathered} 10x-10x>16x-10x-24 \\ 0>6x-24 \end{gathered}[/tex]Add 24 to both sides of the inequality.
[tex]\begin{gathered} 0+24>6x-24+24 \\ 24>6x \end{gathered}[/tex]Divide both sides of the inequality by 6.
[tex]\begin{gathered} \frac{24}{6}>\frac{6x}{6} \\ 4>x \\ \implies x<4 \end{gathered}[/tex]The solution to the inequality is x<4.
