Finite Math Examples

$2 x + 3 < x - 1$ , $3 x - 2 > 2 x + 1$

Step 1

Simplify the first inequality.

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Step 1.1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.1.1

Subtract $x$ from both sides of the inequality.

$2 x + 3 - x < - 1$ and $3 x - 2 > 2 x + 1$

Step 1.1.2

Subtract $x$ from $2 x$ .

$x + 3 < - 1$ and $3 x - 2 > 2 x + 1$

Step 1.2

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

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Step 1.2.1

Subtract $3$ from both sides of the inequality.

$x < - 1 - 3$ and $3 x - 2 > 2 x + 1$

Step 1.2.2

Subtract $3$ from $- 1$ .

$x < - 4$ and $3 x - 2 > 2 x + 1$

Step 2

Simplify the second inequality.

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Step 2.1

Move all terms containing $x$ to the left side of the inequality.

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Step 2.1.1

Subtract $2 x$ from both sides of the inequality.

$x < - 4$ and $3 x - 2 - 2 x > 1$

Step 2.1.2

Subtract $2 x$ from $3 x$ .

$x < - 4$ and $x - 2 > 1$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the inequality.

$x < - 4$ and $x > 1 + 2$

Step 2.2.2

Add $1$ and $2$ .

$x < - 4$ and $x > 3$

Step 3

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

No solution