Solve the compound inequality and give your answer in interval notation. 12x - 4 > 5x + 10 or (-4x+1) + 6 ≥ 8x +72

Question

asked Apr 12, 2023 126k views

1 Answer

Jychan · Answer 1 · 2023-04-18T22:50:28+0000

Answer:

Explanation:

Question 1.

12x-4 > 5x+10

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

Subtract
from both sides of the inequality.

12x-4-5x > 10

Subtract
from
12x .

7x-4 > 10

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

Add 4 to both sides of the inequality.

7x > 14

Divide each term in
7x > 14 by 7 and simplify.

The answer can be written as
x > 2 or (2,∞)

Question 2.

$(-4x+1)+6\geq8x +72$

$-4x+1+6\geq8x +72$

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

Subtract
from both sides of the inequality.

$-12x+7\geq 72$

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

Subtract 7 from both sides of the inequality.

$-12x\geq 65$

Divide each term in
$-12x\geq 65$ by − 12 .

When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$(-12x)/(-12) \leq (65)/(-12)$

The answer can be written as
$x\leq- (65)/(12)$ or (−∞,−
]