Algebra Examples

$6 x - (2 x + 3) > 4 x - 5$

Step 1

Simplify $6 x - (2 x + 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 x - (2 x) - 1 \cdot 3 > 4 x - 5$

Step 1.1.2

Multiply $2$ by $- 1$ .

$6 x - 2 x - 1 \cdot 3 > 4 x - 5$

Step 1.1.3

Multiply $- 1$ by $3$ .

$6 x - 2 x - 3 > 4 x - 5$

Step 1.2

Subtract $2 x$ from $6 x$ .

$4 x - 3 > 4 x - 5$

Step 2

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

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Step 2.1

Subtract $4 x$ from both sides of the inequality.

$4 x - 3 - 4 x > - 5$

Step 2.2

Combine the opposite terms in $4 x - 3 - 4 x$ .

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Step 2.2.1

Subtract $4 x$ from $4 x$ .

$0 - 3 > - 5$

Step 2.2.2

Subtract $3$ from $0$ .

$- 3 > - 5$

Step 3

Since $- 3 > - 5$ , the inequality will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$