Answer:
Part 1) shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]
Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
see the attached figure
Step-by-step explanation:
Part 1) we have
[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Multiply by -10 both sides
[tex]x-2 \leq 6[/tex]
Adds 2 both sides
[tex]x \leq 6+2[/tex]
[tex]x \leq 8[/tex]
The solution is the interval -----> (-∞,8]
All real numbers less than or equal to 8
In a number line the solution is the shaded area at left of x=8 (close circle)
Part 2) we have
[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Multiply by -6 both sides
[tex]100x+11 \leq -489[/tex]
Subtract 11 both sides
[tex]100x \leq -489-11[/tex]
[tex]100x \leq -500[/tex]
Divide by 100 both sides
[tex]x \leq -5[/tex]
The solution is the interval -----> (-∞,-5]
All real numbers less than or equal to -5
In a number line the solution is the shaded area at left of x=-5 (close circle)
Part 3) we have
[tex]\frac{3x}{2}+105 \leq 96[/tex]
Multiply by 2 both sides
[tex]3x+210 \leq 192[/tex]
Subtract 210 both sides
[tex]3x \leq 192-210[/tex]
[tex]3x \leq -18[/tex]
Divide by 3 both sides
[tex]x \leq -18/3[/tex]
[tex]x \leq -6[/tex]
The solution is the interval -----> (-∞,-6]
All real numbers less than or equal to -6
In a number line the solution is the shaded area at left of x=-6 (close circle)
Part 4) we have
[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
Multiply by -18 both sides
[tex]13x-10 \leq 81[/tex]
Adds 10 both sides
[tex]13x \leq 91[/tex]
Divide by 13 both sides
[tex]x \leq 91/13[/tex]
[tex]x \leq 7[/tex]
The solution is the interval -----> (-∞,7]
All real numbers less than or equal to 7
In a number line the solution is the shaded area at left of x=7 (close circle)
