Answer:
[tex]x \leq \dfrac{13}{4}[/tex]
Step-by-step explanation:
Given inequality:
[tex]2x-6(x-3)\geq 5[/tex]
Expand -6(x - 3):
[tex]\implies 2x-6(x)-6(-3)\geq 5[/tex]
[tex]\implies 2x-6x+18\geq 5[/tex]
Combine like terms 2x - 6x = -4x:
[tex]\implies -4x+18\geq 5[/tex]
Subtract 18 from both sides:
[tex]\implies -4x+18-18\geq 5-18[/tex]
[tex]\implies -4x\geq -13[/tex]
Divide both sides by -1, remembering to reverse the inequality:
[tex]\implies\dfrac{ -4x}{-1}\geq \dfrac{-13}{-1}[/tex]
[tex]\implies 4x\leq 13[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x}{4}\leq \dfrac{13}{4}[/tex]
[tex]\implies x \leq \dfrac{13}{4}[/tex]
