Inequalities with Absolute Values: Applying the formula

Solve the inequality:

5-3x>-10

Inequality equations will be solved like a regular equation, except for one rule:

If we multiply the entire equation by a negative, we will reverse the inequality sign.

We start by moving the sections, so that one side has the variables and the other does not:

-3x>-10-5

-3x>-15

Divide by 3

-x>-5

Divide by negative 1 (to get rid of the negative) and remember to reverse the sign of the equation.

x<5

5 > x

Solve the following inequality:

5x+8<9

This is an inequality problem. The inequality is actually an exercise we solve in a completely normal way, except in the case that we multiply or divide by negative.

Let's start by moving the sections:

5X+8<9

5X<9-8

5X<1

We divide by 5:

X<1/5

And this is the solution!

x<\frac{1}{5}

Solve the inequality:

8x+a < 3x-4

Solving an inequality equation is just like a normal equation. We start by trying to isolate the variable (X).

It is important to note that in this equation there are two variables (X and a), so we may not reach a final result.

 8x+a<3x-4

We move the sections

8x-3x<-4-a

We reduce the terms

5x<-4-a

We divide by 5

x< -a/5 -4/5

And this is the solution!

x < -\frac{1}{5}a-\frac{4}{5}

Find when the inequality is satisfied:

-3x+15<3x<4x+8

2.5 < x

When are the following inequalities satisfied?

3x+4<9

3 < x+5

-2 < x < 1\frac{2}{3}

Find a $a$ so that:

0 < 8a+4 ≤ -a+9

$$ -\frac{1}{2} < a ≤ \frac{5}{9}

which value of X satisfies:

8x< 3x+9

but does not exist in:

5x+4<0

$$ -0.8 ≤ x < 1.8

5a+14 < -2x < 3a+8 Calculate X in terms of $a$

given that 0 < a .

No solution