Finite Math Examples

2 x + 3 < x - 1

$2 x + 3 < x - 1$ ,

3 x - 2 > 2 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

$x$ to the left side of the inequality.

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Step 1.1.1

Subtract

x

$x$ from both sides of the inequality.

2 x + 3 - x < - 1

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

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

Step 1.1.2

Subtract

x

$x$ from

2 x

$2 x$ .

x + 3 < - 1

$x + 3 < - 1$ and

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

x + 3 < - 1

$x + 3 < - 1$ and

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

Step 1.2

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 1.2.1

Subtract

3

$3$ from both sides of the inequality.

x < - 1 - 3

$x < - 1 - 3$ and

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

Step 1.2.2

Subtract

3

$3$ from

- 1

$- 1$ .

x < - 4

$x < - 4$ and

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

x < - 4

$x < - 4$ and

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

x < - 4

$x < - 4$ and

3 x - 2 > 2 x + 1

$3 x - 2 > 2 x + 1$

Step 2

Simplify the second inequality.

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Step 2.1

Move all terms containing

x

$x$ to the left side of the inequality.

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Step 2.1.1

Subtract

2 x

$2 x$ from both sides of the inequality.

x < - 4

$x < - 4$ and

3 x - 2 - 2 x > 1

$3 x - 2 - 2 x > 1$

Step 2.1.2

Subtract

2 x

$2 x$ from

3 x

$3 x$ .

x < - 4

$x < - 4$ and

x - 2 > 1

$x - 2 > 1$

x < - 4

$x < - 4$ and

x - 2 > 1

$x - 2 > 1$

Step 2.2

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 2.2.1

Add

2

$2$ to both sides of the inequality.

x < - 4

$x < - 4$ and

x > 1 + 2

$x > 1 + 2$

Step 2.2.2

Add

1

$1$ and

2

$2$ .

x < - 4

$x < - 4$ and

x > 3

$x > 3$

x < - 4

$x < - 4$ and

x > 3

$x > 3$

x < - 4

$x < - 4$ and

x > 3

$x > 3$

Step 3

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

No solution

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$