The solution of the given inequality, 9 x − 1 < 3 4 16 x − 2 , and graph the solution set. The solution set of the given inequality, 9 x − 1 < 3 4 16 x − 2 , is x > 1 6 . Calculation: Consider the given inequality, 9 x − 1 < 3 4 16 x − 2 . Multiply each part by 4 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 . 36 x − 4 < 48 x − 6 Subtract 48 x − 4 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 . − 12 x < − 2 Divide each part by − 12 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 > 1 6 The solution set of the given inequality is the set of all real numbers that are greater than 1 6 , denoted by 1 6 , ∞ . Graph: The solution set of the inequality is shown in the graph. The parenthesis at x = 1 6 means that the solution set does not include the value at x = 1 6 .
The solution of the given inequality, 9 x − 1 < 3 4 16 x − 2 , and graph the solution set. The solution set of the given inequality, 9 x − 1 < 3 4 16 x − 2 , is x > 1 6 . Calculation: Consider the given inequality, 9 x − 1 < 3 4 16 x − 2 . Multiply each part by 4 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 . 36 x − 4 < 48 x − 6 Subtract 48 x − 4 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 . − 12 x < − 2 Divide each part by − 12 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 > 1 6 The solution set of the given inequality is the set of all real numbers that are greater than 1 6 , denoted by 1 6 , ∞ . Graph: The solution set of the inequality is shown in the graph. The parenthesis at x = 1 6 means that the solution set does not include the value at x = 1 6 .
Solution Summary: The author calculates the solution set of the given inequality, 9x-134(16x-2), and graphs it.
To calculate: The solution of the given inequality, 9x−1<3416x−2, and graph the solution set.
The solution set of the given inequality, 9x−1<3416x−2, is x>16.
Calculation:
Consider the given inequality, 9x−1<3416x−2.
Multiply each part by 4 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.
36x−4<48x−6
Subtract 48x−4 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.
−12x<−2
Divide each part by −12 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>16
The solution set of the given inequality is the set of all real numbers that are greater than 16, denoted by 16,∞.
Graph:
The solution set of the inequality is shown in the graph.
The parenthesis at x=16 means that the solution set does not include the value at x=16.
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