Solve the Inequality for x -7(x-2)+1<x

$- 7 (x - 2) + 1 < x$

Step 1

Simplify $- 7 (x - 2) + 1$ .

Simplify each term.

Apply the distributive property.

$- 7 x - 7 \cdot - 2 + 1 < x$

Multiply $- 7$ by $- 2$ .

$- 7 x + 14 + 1 < x$

Add $14$ and $1$ .

$- 7 x + 15 < x$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- 7 x + 15 - x < 0$

Subtract $x$ from $- 7 x$ .

$- 8 x + 15 < 0$

Step 3

Subtract $15$ from both sides of the inequality.

$- 8 x < - 15$

Step 4

Divide each term in $- 8 x < - 15$ by $- 8$ and simplify.

Divide each term in $- 8 x < - 15$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{- 15}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{- 15}{- 8}$

Divide $x$ by $1$ .

$x > \frac{- 15}{- 8}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x > \frac{15}{8}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{15}{8}$

Interval Notation:

$(\frac{15}{8}, \infty)$

Solve the Inequality for x -7(x-2)+1<x

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