Solving Inequalities by Multiplication and Division by a Negative Number

Q.

I know twice as many jokes as my friend does.

Together we know $60$ different jokes.

There are $3$ jokes that both of us know.

How many jokes do I know $?$

How many jokes does my friend knows $?$

Q.

Write an inequality that compares the given numbers. Does the inequality remain true when you multiply each number in the inequality by $2$? By $-2$? Justify your answers. $4;-1$

Q. The symbol of inequality remains same when both sides are multiplied by a negative number.

1. True
2. False

Q. State whether the given statement is true or false:
Dividing each side of an inequality by a negative number changes the direction of the inequality.

1. true
2. false

Q. $-2x>22$ can be simplified as

1. $x<-11$
2. $x<11$
3. $x>-11$

Q. If a variable $x$ satisfy the inequality $-2x+3\ge 11$ and $-x-5\le 7,$ then

1. $4\le x\le 12$
2. $-4\le x\le 12$
3. $-12\le x\le -4$
4. $-12\le x\le 4$

Q. Find the minimum value of $x,$ if $2x+16\le 10x$

Q. Which of the following inequality implies that $x$ is less than or equal to $-2?$

1. $-x\ge -2$
2. $-x\le 2$
3. $-x\le -2$
4. $-x\ge 2$