Solve the System of Inequalities 4x-4<8 and 9x+5>23

and

Step 1
Simplify the first inequality.

Move all terms not containing to the right side of the inequality.

Add to both sides of the inequality.
and
Add and .
and
and
Divide each term in by and simplify.

Divide each term in by .
and
Simplify the left side.

Cancel the common factor of .

Cancel the common factor.
and
Divide by .
and
and
and
Simplify the right side.

Divide by .
and
and
and
and

Step 2
Simplify the second inequality.

Move all terms not containing to the right side of the inequality.

Subtract from both sides of the inequality.
and
Subtract from .
and
and
Divide each term in by and simplify.

Divide each term in by .
and
Simplify the left side.

Cancel the common factor of .

Cancel the common factor.
and
Divide by .
and
and
and
Simplify the right side.

Divide by .
and
and
and
and

Step 3
The intersection consists of the elements that are contained in both intervals.

Step 4
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:

Step 5


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