Pre-Algebra Examples

$4 - 3 x > 7$

Step 1

Move all terms not containing $x$ to the right side of the inequality.

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Step 1.1

Subtract $4$ from both sides of the inequality.

$- 3 x > 7 - 4$

Step 1.2

Subtract $4$ from $7$ .

$- 3 x > 3$

Step 2

Divide each term in $- 3 x > 3$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 x > 3$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $3$ by $- 3$ .

$x < - 1$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$