Question

Can you help me find the answers please

Answer 1

Given:

(a) To determine the inequality for x for the given line.

Inequality:

Since, from the figure, it is obvious that the number line contains an open circle at the point 3.

This means that the end value 3 is not included in the interval.

Hence, the inequality can be written as $x$

Thus, the inequality for x is $x$

(b) Given that $2$ where y is an integer.

We need to determine the possible values of y.

Values of y:

The values of y lie between 2 to 6. Since, the inequality is strictly lesser than, it does not contain the end value.

Therefore, the possible values of y are 3,4,5

(3) Given the inequality $3 x+7>x+19$

We need to solve the inequality.

Solution:

$3 x>x+12$

$2 x>12$

 $x>6$

Thus, the solution of the inequality is $x>6$