The solution of the given inequality, − 9 ≤ − 2 x − 7 < 5 , and graph the solution set. The solution set of the given inequality, − 9 ≤ − 2 x − 7 < 5 , is − 6 < x ≤ 1 . Calculation: Consider the given inequality, − 9 ≤ − 2 x − 7 < 5 . Add 7 from each part by using the property of addition of a constant to an inequality, according to which, if a < b , then a < b becomes a + c < b + c . − 2 ≤ − 2 x < 12 Divide each part by − 2 by using the multiplicative property of an inequality, according to which, if c > 0 , then a < b becomes a c < b c and if c < 0 , then a > b becomes a c < b c . − 6 < x ≤ 1 The solution set of the given inequality is the set of all real numbers that are greater than − 6 and less than or equal to 1 which can be denoted by − 6 , 1 . Graph: The solution set of the inequality is shown in the graph. The parenthesis at x = − 6 means that this point is not included in the solution set. The bracket at x = 1 means that this point is included in the solution set.
The solution of the given inequality, − 9 ≤ − 2 x − 7 < 5 , and graph the solution set. The solution set of the given inequality, − 9 ≤ − 2 x − 7 < 5 , is − 6 < x ≤ 1 . Calculation: Consider the given inequality, − 9 ≤ − 2 x − 7 < 5 . Add 7 from each part by using the property of addition of a constant to an inequality, according to which, if a < b , then a < b becomes a + c < b + c . − 2 ≤ − 2 x < 12 Divide each part by − 2 by using the multiplicative property of an inequality, according to which, if c > 0 , then a < b becomes a c < b c and if c < 0 , then a > b becomes a c < b c . − 6 < x ≤ 1 The solution set of the given inequality is the set of all real numbers that are greater than − 6 and less than or equal to 1 which can be denoted by − 6 , 1 . Graph: The solution set of the inequality is shown in the graph. The parenthesis at x = − 6 means that this point is not included in the solution set. The bracket at x = 1 means that this point is included in the solution set.
Solution Summary: The author calculates the solution of the given inequality, -9le -2x-75, and graphs its solution set.
To calculate: The solution of the given inequality, −9≤−2x−7<5, and graph the solution set.
The solution set of the given inequality, −9≤−2x−7<5, is −6<x≤1.
Calculation:
Consider the given inequality, −9≤−2x−7<5.
Add 7 from each part by using the property of addition of a constant to an inequality, according to which, if a<b, then a<b becomes a+c<b+c.
−2≤−2x<12
Divide each part by −2 by using the multiplicative property of an inequality, according to which, if c>0, then a<b becomes ac<bc and if c<0, then a>b becomes ac<bc.
−6<x≤1
The solution set of the given inequality is the set of all real numbers that are greater than −6 and less than or equal to 1 which can be denoted by −6,1.
Graph:
The solution set of the inequality is shown in the graph.
The parenthesis at x=−6 means that this point is not included in the solution set.
The bracket at x=1 means that this point is included in the solution set.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.