Which set of values for x makes the inequality 12−x<7 true

Mathematics

1 answer:

kozerog [31]2 years ago

7 0

Answer:

$\{x:x>5\}$

Step-by-step explanation:

Given

$12 - x < 7$

Required

Values of x that make it true

First: solve the inequality.

$12 - x < 7$

Collect Like Terms

$- x < 7-12$

$- x < -5$

Multiply both sides by -1

$-1 * - x < -5 * -1$

$x > 5$ --- The inequality changes when multiplied by a negative value

So, the solution implies that the value of x is greater than 5 (i.e. 6, 7, 8..)

Hence, the set is:

$\{x:x>5\}$

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1. The event $A\cap B$ consists in selecting two slips, first is 3 and second should be 1, because the sum is 4. The number of favorable outcomes is exactly 1 and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event $A\cap B$ is

$Pr(A\cap B)=\dfrac{1}{20}.$

2. The event $B$ consists in selecting two slips with the sum 4. The number of favorable outcomes is exactly 2 (1st slip 3 and 2nd slip 1 or 1st slip 1 and 2nd slip 3) and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event $B$ is