Solve the Inequality for x 5(x+1)-10>=2x+3(x+2)

$5 (x + 1) - 10 \geq 2 x + 3 (x + 2)$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$2 x + 3 (x + 2) \leq 5 (x + 1) - 10$

Step 2

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

Simplify each term.

Apply the distributive property.

$2 x + 3 x + 3 \cdot 2 \leq 5 (x + 1) - 10$

Multiply $3$ by $2$ .

$2 x + 3 x + 6 \leq 5 (x + 1) - 10$

Add $2 x$ and $3 x$ .

$5 x + 6 \leq 5 (x + 1) - 10$

Step 3

Simplify $5 (x + 1) - 10$ .

Simplify each term.

Apply the distributive property.

$5 x + 6 \leq 5 x + 5 \cdot 1 - 10$

Multiply $5$ by $1$ .

$5 x + 6 \leq 5 x + 5 - 10$

Subtract $10$ from $5$ .

$5 x + 6 \leq 5 x - 5$

Step 4

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

Subtract $5 x$ from both sides of the inequality.

$5 x + 6 - 5 x \leq - 5$

Combine the opposite terms in $5 x + 6 - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 + 6 \leq - 5$

Add $0$ and $6$ .

$6 \leq - 5$

Step 5

Since $6 \neq - 5$ , there are no solutions.

No solution