High School

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Which graph represents the solution to this inequality?

A. A straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passing through minus 5.

B. A straight line passing from minus 17 to minus 5. A ray with a red line starting at point minus 13 and passing through minus 17.

C. A straight line passing from minus 17 to minus 5. A ray with a red dot at minus 13, passing through minus 5.

D. A straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passing through minus 17.

Answer :

The graph which represents the solution to given inequality -1/4(12x+8) <-2x+11 is option C. A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5

What is an inequality and how can we solve it ?

An inequality is an equation which compares two expressions where either one is greater than or less than or greater than equal to or less than equal to from another one.

To solve inequalities: we can add some number (positive or negative) to both sides of the without changing the inequality sign.

We can divide both sides by a positive number no change of sign of inequality

We can divide both sides by a negative number but we have to change sign of inequality.

Given inequality is

-1/4(12x+8) <-2x+11

⇒-3x -2 < -2x +11

Adding 2 both sides, we get

⇒ -3x < -2x +13

Adding 2x both sides , we get

⇒2x-3x < 2x-2x+13

⇒ -x < 13

Multiply both sides by (-1)

⇒ (-1)(-x)> -13 ( multiplied by negative number so sign is reversed)

⇒ x >-13

Therefore , the solution to given inequality is all real numbers greater than -13, thus answer is option C. A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5 ( as it has all number right to -13 included in the solution)

Also, learn more about inequalities from below link:

https://brainly.com/question/18929468

#SPJ1

The complete question can be found below:

Which graph represents the solution to this inequality? -1/4(12x+8) <-2x+11 A. A straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passes through minus 5

B. A straight line passing from minus 17 to minus 5. A ray with a red line starts at point minus 13 and passes through minus 17

C. A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5

D. A straight line passing from minus 17 to minus 5. A ray with a red dot at point minus 9 and passes through minus 17

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