Algebra Examples

$2 (7 a - 1) - 11 a \geq 3 (a - 4)$

Step 1

Simplify $2 (7 a - 1) - 11 a$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$2 (7 a) + 2 \cdot - 1 - 11 a \geq 3 (a - 4)$

Step 1.1.2

Multiply $7$ by $2$ .

$14 a + 2 \cdot - 1 - 11 a \geq 3 (a - 4)$

Step 1.1.3

Multiply $2$ by $- 1$ .

$14 a - 2 - 11 a \geq 3 (a - 4)$

Step 1.2

Subtract $11 a$ from $14 a$ .

$3 a - 2 \geq 3 (a - 4)$

Step 2

Simplify $3 (a - 4)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$3 a - 2 \geq 3 a + 3 \cdot - 4$

Step 2.2

Multiply $3$ by $- 4$ .

$3 a - 2 \geq 3 a - 12$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $3 a$ from both sides of the inequality.

$3 a - 2 - 3 a \geq - 12$

Step 3.2

Combine the opposite terms in $3 a - 2 - 3 a$ .

Tap for more steps...

Step 3.2.1

Subtract $3 a$ from $3 a$ .

$0 - 2 \geq - 12$

Step 3.2.2

Subtract $2$ from $0$ .

$- 2 \geq - 12$

Step 4

Since $- 2 \geq - 12$ , the inequality will always be true.

Always true

Step 5

Convert the inequality to interval notation.

$[3 (a - 4), \infty)$

Step 6