Trigonometry Examples

$5 (1 - 4 x) + 14 x < 3 (5 - 2 x)$

Step 1

Simplify $5 (1 - 4 x) + 14 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 \cdot 1 + 5 (- 4 x) + 14 x < 3 (5 - 2 x)$

Step 1.1.2

Multiply $5$ by $1$ .

$5 + 5 (- 4 x) + 14 x < 3 (5 - 2 x)$

Step 1.1.3

Multiply $- 4$ by $5$ .

$5 - 20 x + 14 x < 3 (5 - 2 x)$

Step 1.2

Add $- 20 x$ and $14 x$ .

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

Step 2

Simplify $3 (5 - 2 x)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $5$ .

$5 - 6 x < 15 + 3 (- 2 x)$

Step 2.2.2

Multiply $- 2$ by $3$ .

$5 - 6 x < 15 - 6 x$

Step 3

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

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Step 3.1

Add $6 x$ to both sides of the inequality.

$5 - 6 x + 6 x < 15$

Step 3.2

Combine the opposite terms in $5 - 6 x + 6 x$ .

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Step 3.2.1

Add $- 6 x$ and $6 x$ .

$5 + 0 < 15$

Step 3.2.2

Add $5$ and $0$ .

$5 < 15$

Step 4

Since $5 < 15$ , the inequality will always be true.

Always true

Step 5