Algebra Examples

$(3 + x) + 7 < 2 x$

Step 1

Add $3$ and $7$ .

$x + 10 < 2 x$

Step 2

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

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Step 2.1

Subtract $2 x$ from both sides of the inequality.

$x + 10 - 2 x < 0$

Step 2.2

Subtract $2 x$ from $x$ .

$- x + 10 < 0$

Step 3

Subtract $10$ from both sides of the inequality.

$- x < - 10$

Step 4

Divide each term in $- x < - 10$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x < - 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 10}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 10}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x > \frac{- 10}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 10$ by $- 1$ .

$x > 10$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 10$

Interval Notation:

$(10, \infty)$