Algebra Examples

$6 (5 x + 1) - 6 < 5 (6 x - 5) + 7$

Step 1

Simplify $6 (5 x + 1) - 6$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 (5 x) + 6 \cdot 1 - 6 < 5 (6 x - 5) + 7$

Step 1.1.2

Multiply $5$ by $6$ .

$30 x + 6 \cdot 1 - 6 < 5 (6 x - 5) + 7$

Step 1.1.3

Multiply $6$ by $1$ .

$30 x + 6 - 6 < 5 (6 x - 5) + 7$

Step 1.2

Combine the opposite terms in $30 x + 6 - 6$ .

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Step 1.2.1

Subtract $6$ from $6$ .

$30 x + 0 < 5 (6 x - 5) + 7$

Step 1.2.2

Add $30 x$ and $0$ .

$30 x < 5 (6 x - 5) + 7$

Step 2

Simplify $5 (6 x - 5) + 7$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$30 x < 5 (6 x) + 5 \cdot - 5 + 7$

Step 2.1.2

Multiply $6$ by $5$ .

$30 x < 30 x + 5 \cdot - 5 + 7$

Step 2.1.3

Multiply $5$ by $- 5$ .

$30 x < 30 x - 25 + 7$

Step 2.2

Add $- 25$ and $7$ .

$30 x < 30 x - 18$

Step 3

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

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Step 3.1

Subtract $30 x$ from both sides of the inequality.

$30 x - 30 x < - 18$

Step 3.2

Subtract $30 x$ from $30 x$ .

$0 < - 18$

Step 4

Since $0 > - 18$ , there are no solutions.

No solution