Solving Inequalities by Multiplication and Division by a Negative Number

Q.

When you multiply or divide each side of an inequality by the same negative number, you must reverse the direction of the inequality symbol. Explain why?

Q. Solve for $x$ : $-\frac{x}{5}>-2$

$x<$

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

Q. Which of the following is the simplified form of $\frac{-4x}{10}\ge \frac{32}{5}$?

1. $x\le 16$
2. $x\le -16$
3. $x\ge 16$
4. $x\ge -16$

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. $-x\ge 2$

Q.

Solve the inequality. Graph the solution.

$-1.2b-5.3\ge 1.9$

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. Solve for $x$ : $-2x>6$

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

Q.

Write the inequality modeled by the algebra tiles. Then solve the inequality using algebra tiles. Check your answer using properties of inequality.