Pre-Algebra Examples

$3 x - 4 < 7 x - 5 x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$7 x - 5 x > 3 x - 4$

Step 2

Subtract $5 x$ from $7 x$ .

$2 x > 3 x - 4$

Step 3

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

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Step 3.1

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

$2 x - 3 x > - 4$

Step 3.2

Subtract $3 x$ from $2 x$ .

$- x > - 4$

Step 4

Divide each term in $- x > - 4$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x > - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 4}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 4}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x < \frac{- 4}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 4$ by $- 1$ .

$x < 4$

Step 5