Algebra Examples

$6 (x + 5) - 7 \leq 8 x + 1$

Step 1

Simplify $6 (x + 5) - 7$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 x + 6 \cdot 5 - 7 \leq 8 x + 1$

Step 1.1.2

Multiply $6$ by $5$ .

$6 x + 30 - 7 \leq 8 x + 1$

Step 1.2

Subtract $7$ from $30$ .

$6 x + 23 \leq 8 x + 1$

Step 2

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

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Step 2.1

Subtract $8 x$ from both sides of the inequality.

$6 x + 23 - 8 x \leq 1$

Step 2.2

Subtract $8 x$ from $6 x$ .

$- 2 x + 23 \leq 1$

Step 3

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

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Step 3.1

Subtract $23$ from both sides of the inequality.

$- 2 x \leq 1 - 23$

Step 3.2

Subtract $23$ from $1$ .

$- 2 x \leq - 22$

Step 4

Divide each term in $- 2 x \leq - 22$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x \leq - 22$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 22}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 22}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 22}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 22$ by $- 2$ .

$x \geq 11$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 11$

Interval Notation:

$[11, \infty)$