Pre-Algebra Examples

$3 x - 4 < 7 x$

Step 1

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

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Step 1.1

Subtract $7 x$ from both sides of the inequality.

$3 x - 4 - 7 x < 0$

Step 1.2

Subtract $7 x$ from $3 x$ .

$- 4 x - 4 < 0$

Step 2

Add $4$ to both sides of the inequality.

$- 4 x < 4$

Step 3

Divide each term in $- 4 x < 4$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 x < 4$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{4}{- 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{4}{- 4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{4}{- 4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $4$ by $- 4$ .

$x > - 1$

Step 4