# algebra

Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Explain why or why not? Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.

1. 👍
2. 👎
3. 👁
1. take any true inequality, say ...

4 < 10
now multiply both sides by 10
40 < 100 , still true
divide original by 2
2 < 5 , still true

multiply original by -10
-40 < -100 , FALSE!, how do we make it true ?
-40 > -100

divide original by -2
-2 < -5 , FALSE! , how do we make it true?
-2 > -5

5 = 5 , true
multiply by -1
-5 = -5, (did you notice how I switched the = sign from = to = ?? , lol)

1. 👍
2. 👎
2. Another way to think of this changing direction stuff is to leave the direction the same, and move the expressions. Suppose you have

-3x > 9

Rather than dividing by -3, let's get rid of the negative coefficient by adding and subtracting.

-3x + 3x > 9 + 3x
0 > 9 + 3x

Now subtarct 9 from both sides

0 - 9 > 9 + 3x - 9
-9 > 3x

Now divide by +3 to get

-3 > x

So, what we have is

-3x > 9 changes to
-3 > x

and even though we haven't change direction of the actual symbol, we have done it logically by moving things to the other side of the arrow.

1. 👍
2. 👎

## Similar Questions

1. ### algebra

Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality for your classmates to solve. In your inequality, use both

2. ### d/dx

d/dx( ln |sin(pi/x)| ) = ? Thanks. If those are absolute value signs, the derivative will not exist when sin (pi/x) = 0, because of the sign change that occurs there. Assume sin (pi/x) > 0 Let u(x) = pi/x and v(x) = sin x, and use

3. ### Math

1. solve the equation. -9v - 5 = -95 A. 17 B. 11 C. 10 ** D. -10 2. Solve the equation. X/4 - 5 = -8 A. -27 B. -12 ** C. -7 D. 12 3. Solve the equation. d/3 + 10 = 7 A. 51 B. 20 ** C. 0 D. -9 4. Solve the equation. 2(2 - 2k) = -3k

4. ### Algebra Linear Inequalities Help

Select among the following the two operations that will not change the direction of an inequality.(1 point) A negative number is added to both sides of an inequality. A negative number is subtracted from both sides of an

1. ### Estimation decimal quotient

Use compatible numbers to find the each quotient ,2.90 divided by 29,48 divided by 3.2, 0.18 divided by 0.33,152 divided by 5.12,41.9 divided by 19,33.90 divided by 10.2, 502 divided by 9.5, 180.8 divided by 6 , 48 divided by

2. ### math

When multiplying or dividing by a negative number, the inequality sign must be ___. 1. removed 2. flipped

3. ### Algebra

1. Why does the inequality sign change when both sides of the inequality are multiplied or divided by a negative number? Does this happen with equations? Why or why not? 2. Write an inequality for your classmates to solve. In your

1. ### math

Complete each statement to identify the sign. Part A The sign of the product of two negative numbers is A. positive. B. negative. Part B The sign of the quotient of numbers with opposite signs is A. positive B. negative.

2. ### Math

Can someone please help me with an algebra problem? -|4-8b|=12 I really get confused with the absolute value symbols and a negative sign outside of them. Don't worry about it; it does tend to be a bit confusing. I'll explain the

3. ### Variable

SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES Solve the equation. Then check your solution. 4x-9 = 7x+12 Just remember that one can add, subtract, multiply, divide, etc but whatever is done to one side must be done to the

4. ### math

according to the triangle inequality, the length of the longest side of a triangle bust be less than the sum of the lengths of the other two sides. the two shortest sides of a triangle measure 3/10 and x + 1/5 and the longest