How do you solve and graph # -3 ≤ 3 - 2x

Question

How do you solve and graph #  -3 ≤ 3 - 2x< 11#?

Kennedy Adams · Accepted Answer

See a solution process below:

First, subtract #color(red)(3)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced: #-color(red)(3) - 3 <= -color(red)(3) + 3 - 2x < -color(red)(3) + 11# #-6 <= 0 - 2x < 8# #-6 <= -2x < 8# Now, divide each segment by #color(blue)(-2)# to solve for #x# while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators: #(-6)/color(blue)(-2) color(red)(>=) (-2x)/color(blue)(-2) color(red)(>) 8/color(blue)(-2)# #3 color(red)(>=) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>) -4# #3 color(red)(>=) x color(red)(>) -4# Or #x > -4# and #x <= 3# Or, in interval notation: #(-4, 3]#

Eva Abramson · Answer

undefined To solve and graph the compound inequality $ -3 \leq 3 - 2x < 11 $, follow these steps: 1. Begin by solving each inequality separately: - Solve $ -3 \leq 3 - 2x $ - Solve $ 3 - 2x < 11 $ 2. Solve the first inequality: $$ -3 \leq 3 - 2x $$ $$ -3 - 3 \leq -2x $$ $$ -6 \leq -2x $$ $$ -6/-2 \geq x $$ $$ 3 \geq x $$ 3. Solve the second inequality: $$ 3 - 2x < 11 $$ $$ -2x < 11 - 3 $$ $$ -2x < 8 $$ $$ -2x/-2 > 8/-2 $$ $$ x > -4 $$ 4. Combine the solutions: $$ -6 \leq -2x \leq 3 $$ $$ -4 < x < 3 $$ 5. Graph the solution on a number line: - Place an open circle at $ x = -4 $ and $ x = 3 $ to indicate that they are not included in the solution. - Shade the region between $ x = -4 $ and $ x = 3 $ to represent the values of $ x $ that satisfy the compound inequality. The graph should show an open circle at $ x = -4 $ and $ x = 3 $, with shading between these two points on the number line.

How do you solve and graph # -3 ≤ 3 - 2x&lt; 11#?

How do you solve and graph # -3 ≤ 3 - 2x< 11#?