Answer:
[tex]x<\frac{6}{5}[/tex]
Refer to picture for number line
Step-by-step explanation:
To solve this inequality, we want to isolate the variable. We can do this my getting like terms onto one side
[tex]6x-7<2-\frac{3x}{2}[/tex] [add both sides by 7]
[tex]6x<9-\frac{3x}{2}[/tex] [add both sides by 3x/2]
[tex]6x+\frac{3x}{2}<9[/tex] [multiply both sides by 2]
[tex]12x+3x<18[/tex] [add]
[tex]15x<18[/tex] [divide both sides by 15]
[tex]x<\frac{18}{15}[/tex] [simplify]
[tex]x<\frac{6}{5}[/tex]
Now that we have out inequality, we want to graph it. Since we know that [tex]x<\frac{6}{5}[/tex], that means we have an open circle. Since x is less than, the arrow would be pointing left.
