Solve for x 5x-2(x-1)+11<4x-3(x-2)+5

$5 x - 2 (x - 1) + 11 < 4 x - 3 (x - 2) + 5$

Step 1

Simplify $5 x - 2 (x - 1) + 11$ .

Simplify each term.

Apply the distributive property.

$5 x - 2 x - 2 \cdot - 1 + 11 < 4 x - 3 (x - 2) + 5$

Multiply $- 2$ by $- 1$ .

$5 x - 2 x + 2 + 11 < 4 x - 3 (x - 2) + 5$

Simplify by adding terms.

Subtract $2 x$ from $5 x$ .

$3 x + 2 + 11 < 4 x - 3 (x - 2) + 5$

Add $2$ and $11$ .

$3 x + 13 < 4 x - 3 (x - 2) + 5$

Step 2

Simplify $4 x - 3 (x - 2) + 5$ .

Simplify each term.

Apply the distributive property.

$3 x + 13 < 4 x - 3 x - 3 \cdot - 2 + 5$

Multiply $- 3$ by $- 2$ .

$3 x + 13 < 4 x - 3 x + 6 + 5$

Simplify by adding terms.

Subtract $3 x$ from $4 x$ .

$3 x + 13 < x + 6 + 5$

Add $6$ and $5$ .

$3 x + 13 < x + 11$

Step 3

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

Subtract $x$ from both sides of the inequality.

$3 x + 13 - x < 11$

Subtract $x$ from $3 x$ .

$2 x + 13 < 11$

Step 4

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

Subtract $13$ from both sides of the inequality.

$2 x < 11 - 13$

Subtract $13$ from $11$ .

$2 x < - 2$

Step 5

Divide each term in $2 x < - 2$ by $2$ and simplify.

Divide each term in $2 x < - 2$ by $2$ .

$\frac{2 x}{2} < \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 2}{2}$

Divide $x$ by $1$ .

$x < \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$x < - 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$

Solve for x 5x-2(x-1)+11<4x-3(x-2)+5

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