Algebra Examples

$3 (4 x - (2 x - 7)) < 2 (3 x - 5)$

Step 1

Simplify $3 (4 x - (2 x - 7))$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (4 x - (2 x - 7)) < 2 (3 x - 5)$

Step 1.2

Simplify by adding zeros.

$3 (4 x - (2 x - 7)) < 2 (3 x - 5)$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$3 (4 x - (2 x) - - 7) < 2 (3 x - 5)$

Step 1.3.2

Multiply $2$ by $- 1$ .

$3 (4 x - 2 x - - 7) < 2 (3 x - 5)$

Step 1.3.3

Multiply $- 1$ by $- 7$ .

$3 (4 x - 2 x + 7) < 2 (3 x - 5)$

$3 (4 x - 2 x + 7) < 2 (3 x - 5)$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $2 x$ from $4 x$ .

$3 (2 x + 7) < 2 (3 x - 5)$

Step 1.4.2

Apply the distributive property.

$3 (2 x) + 3 \cdot 7 < 2 (3 x - 5)$

Step 1.4.3

Multiply.

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Step 1.4.3.1

Multiply $2$ by $3$ .

$6 x + 3 \cdot 7 < 2 (3 x - 5)$

Step 1.4.3.2

Multiply $3$ by $7$ .

$6 x + 21 < 2 (3 x - 5)$

$6 x + 21 < 2 (3 x - 5)$

$6 x + 21 < 2 (3 x - 5)$

$6 x + 21 < 2 (3 x - 5)$

Step 2

Simplify $2 (3 x - 5)$ .

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Step 2.1

Apply the distributive property.

$6 x + 21 < 2 (3 x) + 2 \cdot - 5$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $2$ .

$6 x + 21 < 6 x + 2 \cdot - 5$

Step 2.2.2

Multiply $2$ by $- 5$ .

$6 x + 21 < 6 x - 10$

$6 x + 21 < 6 x - 10$

$6 x + 21 < 6 x - 10$

Step 3

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

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Step 3.1

Subtract $6 x$ from both sides of the inequality.

$6 x + 21 - 6 x < - 10$

Step 3.2

Combine the opposite terms in $6 x + 21 - 6 x$ .

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Step 3.2.1

Subtract $6 x$ from $6 x$ .

$0 + 21 < - 10$

Step 3.2.2

Add $0$ and $21$ .

$21 < - 10$

$21 < - 10$

$21 < - 10$

Step 4

Since $21 > - 10$ , there are no solutions.

No solution

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