The solution of the given inequality, 3 + 2 x 7 > x − 2 , and graph the solution set. The solution set of the given inequality, 3 + 2 x 7 > x − 2 , is x < 7 . Calculation: Consider the given inequality, 3 + 2 x 7 > x − 2 . Multiply each part by 7 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 . 21 + 2 x > 7 x − 14 Subtract 7 x and 21 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 . − 5 x > − 35 Divide each part by − 5 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 . x < 7 The solution set of the inequality is the set of all real numbers that are less than 7 which can be denoted by − ∞ , 7 . Graph: The solution set of the inequality is shown in the graph. The parenthesis at x = 7 means that the value at x = 7 is not included in the solution set of the given inequality.
The solution of the given inequality, 3 + 2 x 7 > x − 2 , and graph the solution set. The solution set of the given inequality, 3 + 2 x 7 > x − 2 , is x < 7 . Calculation: Consider the given inequality, 3 + 2 x 7 > x − 2 . Multiply each part by 7 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 . 21 + 2 x > 7 x − 14 Subtract 7 x and 21 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 . − 5 x > − 35 Divide each part by − 5 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 . x < 7 The solution set of the inequality is the set of all real numbers that are less than 7 which can be denoted by − ∞ , 7 . Graph: The solution set of the inequality is shown in the graph. The parenthesis at x = 7 means that the value at x = 7 is not included in the solution set of the given inequality.
Solution Summary: The author calculates the solution set of the given inequality, 3+2x7>x-2, and graphs it. The parenthesis at x=7 means that the value at
To calculate: The solution of the given inequality, 3+2x7>x−2, and graph the solution set.
The solution set of the given inequality, 3+2x7>x−2, is x<7.
Calculation:
Consider the given inequality, 3+2x7>x−2.
Multiply each part by 7 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.
21+2x>7x−14
Subtract 7x and 21 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.
−5x>−35
Divide each part by −5 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.
x<7
The solution set of the inequality is the set of all real numbers that are less than 7 which can be denoted by −∞,7.
Graph:
The solution set of the inequality is shown in the graph.
The parenthesis at x=7 means that the value at x=7 is not included in the solution set of the given inequality.
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