Algebra Examples

$7 (x + 1) < 5 x + 1 - 4 x$

Step 1

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

$5 x + 1 - 4 x > 7 (x + 1)$

Step 2

Subtract $4 x$ from $5 x$ .

$x + 1 > 7 (x + 1)$

Step 3

Simplify $7 (x + 1)$ .

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Step 3.1

Apply the distributive property.

$x + 1 > 7 x + 7 \cdot 1$

Step 3.2

Multiply $7$ by $1$ .

$x + 1 > 7 x + 7$

Step 4

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

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Step 4.1

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

$x + 1 - 7 x > 7$

Step 4.2

Subtract $7 x$ from $x$ .

$- 6 x + 1 > 7$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the inequality.

$- 6 x > 7 - 1$

Step 5.2

Subtract $1$ from $7$ .

$- 6 x > 6$

Step 6

Divide each term in $- 6 x > 6$ by $- 6$ and simplify.

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Step 6.1

Divide each term in $- 6 x > 6$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} < \frac{6}{- 6}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 6$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} < \frac{6}{- 6}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x < \frac{6}{- 6}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $6$ by $- 6$ .

$x < - 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$