Choose the correct solution and graph for the inequality.
2x-2 < -12 or 2x+3>7

(1 point)
Responses

 or 
Just to the left of negative 4, is an open circle. The number line is shaded to the left of the open circle. Halfway between 0 and positive 4 is an open circle. The number line is shaded to the right of the open circle.
Image with alt text: x less than negative 5 or Image with alt text: x greater than 2 Image with alt text: A number line has an open circle at negative 5 and is filled in to the left and another open circle at 2 and is filled in to the right. Just to the left of negative 4, is an open circle. The number line is shaded to the left of the open circle. Halfway between 0 and positive 4 is an open circle. The number line is shaded to the right of the open circle.

 or 
Just to the left of negative 4, is an open circle. The number line is shaded to the left of the open circle. Just to the right of positive 4, is an open circle. The number line is shaded to the right of the open circle.
Image with alt text: x less than negative 5 or Image with alt text: x greater than 5 Image with alt text: A number line has an open circle at negative 5 and is filled in to the left and another open circle at 5 and is filled in to the right. Just to the left of negative 4, is an open circle. The number line is shaded to the left of the open circle. Just to the right of positive 4, is an open circle. The number line is shaded to the right of the open circle.

 or 
Just to the right of negative 8, is an open circle. The number line is shaded to the left of the open circle. Just to the right of positive 4, is an open circle. The number line is shaded to the right of the open circle.
Image with alt text: x less-than negative 7 or Image with alt text: x greater than 5 Image with alt text: A number line has an open circle at negative 7 and is filled in to the left and another open circle at 5 and is filled in to the right. Just to the right of negative 8, is an open circle. The number line is shaded to the left of the open circle. Just to the right of positive 4, is an open circle. The number line is shaded to the right of the open circle.

 or 

Just to the left of negative 4, is an open circle. The number line is shaded to the left of the open circle. Just to the right of positive 4, is an open circle. The number line is shaded to the right of the open circle.
Image with alt text: x less than negative 5 or Image with alt text: x greater than 5
Image with alt text: A number line has an open circle at negative 5 and is filled in to the left and another open circle at 5 and is filled in to the right. Just to the left of negative 4, is an open circle. The number line is shaded to the left of the open circle. Just to the right of positive 4, is an open circle. The number line is shaded to the right of the open circle.
Solution:  or 
The correct solution and graph for the inequality 2x-2 < -12 or 2x+3>7 is:
Just to the left of negative 4, there is an open circle. The number line is shaded to the left of the open circle. Halfway between 0 and positive 4, there is an open circle. The number line is shaded to the right of the open circle.
Image: x less than negative 5 and x greater than 2
A number line has an open circle at negative 5 and is filled in to the left, and another open circle at 2 and is filled in to the right. Just to the left of negative 4, there is an open circle. The number line is shaded to the left of the open circle. Halfway between 0 and positive 4, there is an open circle. The number line is shaded to the right of the open circle.
The correct solution and graph for the inequality 2x-2 < -12 or 2x+3 > 7 is:
Image with alt text: x less than -5 or x greater than 2
Image with alt text: A number line has an open circle at -5 and is filled in to the left, and another open circle at 2 and is filled in to the right.
To solve this inequality, we will solve the two individual inequalities separately and then combine the solutions.
For the first inequality, 2x-2 < -12:
1. Add 2 to both sides of the inequality: 2x-2+2 < -12+2
Simplifying, we have: 2x < -10
2. Divide both sides of the inequality by 2 (since the coefficient of x is 2): 2x/2 < -10/2
Simplifying, we have: x < -5
For the second inequality, 2x+3 > 7:
1. Subtract 3 from both sides of the inequality: 2x+3-3 > 7-3
Simplifying, we have: 2x > 4
2. Divide both sides of the inequality by 2 (since the coefficient of x is 2): 2x/2 > 4/2
Simplifying, we have: x > 2
Now, we have the solutions for each inequality: x < -5 and x > 2.
To graph the combined solution, we will plot an open circle at -5 on the number line and shade to the left of the open circle to represent x < -5. Then, we will plot an open circle at 2 and shade to the right of the open circle to represent x > 2.
The correct solution and graph for the inequality is shown in the first option: Image with alt text: x less than -5 or x greater than 2. The number line has an open circle at -5 and is filled in to the left, and another open circle at 2 and is filled in to the right.