Algebra Examples

$\frac{3 x - 4}{3} < x$

Step 1

Multiply both sides by $3$ .

$\frac{3 x - 4}{3} \cdot 3 < x \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 x - 4}{3} \cdot 3 < x \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$3 x - 4 < x \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Move $3$ to the left of $x$ .

$3 x - 4 < 3 x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $3 x$ from both sides of the inequality.

$3 x - 4 - 3 x < 0$

Step 3.1.2

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

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Step 3.1.2.1

Subtract $3 x$ from $3 x$ .

$0 - 4 < 0$

Step 3.1.2.2

Subtract $4$ from $0$ .

$- 4 < 0$

Step 3.2

Since $- 4 < 0$ , the inequality will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$