How do you solve -5\geq - 2x + 11\geq - 952x+119?

2 Answers
May 19, 2017

See a solution process below:

Explanation:

First, subtract color(red)(11)11 from each segment of the system of inequalities to isolate the xx term while keeping the system balanced:

-5 - color(red)(11) >= -2x + 11 - color(red)(11) >= -9 - color(red)(11)5112x+1111911

-16 >= -2x + 0 >= -20162x+020

-16 >= -2x >= -20162x20

Now, divide each segment by color(blue)(-2)2 to solve for xx while keeping the system balanced. However, because we are multiplying or dividing an inequality by a negative numbers we must also reverse the inequality operators:

(-16)/color(blue)(-2) color(red)(<=) (-2x)/color(blue)(-2) color(red)(<=) (-20)/color(blue)(-2)1622x2202

8 color(red)(<=) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) 10

8 color(red)(<=) x color(red)(<=) 10

Or

x >= 8 and x <= 10

Or, in interval notation:

[8, 10]

May 19, 2017

Subtract 11 from everything
Divide everything by -2 (remember to "flip" the inequalities)

Explanation:

Given: -5>=- 2x + 11>= - 9

Subtract 11 from everything:

-16>=- 2x>= -20

Divide everything by -2:

8<=x<= 10