Solve the Inequality for x -5-3x>=2(10+2x)+3

$- 5 - 3 x \geq 2 (10 + 2 x) + 3$

Step 1

Simplify $2 (10 + 2 x) + 3$ .

Simplify each term.

Apply the distributive property.

$- 5 - 3 x \geq 2 \cdot 10 + 2 (2 x) + 3$

Multiply $2$ by $10$ .

$- 5 - 3 x \geq 20 + 2 (2 x) + 3$

Multiply $2$ by $2$ .

$- 5 - 3 x \geq 20 + 4 x + 3$

Add $20$ and $3$ .

$- 5 - 3 x \geq 4 x + 23$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$- 5 - 3 x - 4 x \geq 23$

Subtract $4 x$ from $- 3 x$ .

$- 5 - 7 x \geq 23$

Step 3

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

Add $5$ to both sides of the inequality.

$- 7 x \geq 23 + 5$

Add $23$ and $5$ .

$- 7 x \geq 28$

Step 4

Divide each term in $- 7 x \geq 28$ by $- 7$ and simplify.

Divide each term in $- 7 x \geq 28$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} \leq \frac{28}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} \leq \frac{28}{- 7}$

Divide $x$ by $1$ .

$x \leq \frac{28}{- 7}$

Simplify the right side.

Divide $28$ by $- 7$ .

$x \leq - 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 4$

Interval Notation:

$(- \infty, - 4]$

Solve the Inequality for x -5-3x>=2(10+2x)+3

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