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 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.
The correct solution and graph for the given inequality are:
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 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.
To solve the inequality 2x - 2 < -12, we can follow these steps:
1. Add 2 to both sides of the inequality: 2x - 2 + 2 < -12 + 2
Simplifying this gives us: 2x < -10.
2. Divide both sides of the inequality by 2: (2x)/2 < (-10)/2.
This simplifies to: x < -5.
So, the correct solution for the first inequality is x < -5.
To solve the second inequality 2x + 3 > 7, we can follow these steps:
1. Subtract 3 from both sides of the inequality: 2x + 3 - 3 > 7 - 3.
Simplifying this gives us: 2x > 4.
2. Divide both sides of the inequality by 2: (2x)/2 > (4)/2.
This simplifies to: x > 2.
So, the correct solution for the second inequality is x > 2.
Now, we need to represent these solutions on a number line:
- We mark an open circle at -5 and shade to the left of the open circle to represent x < -5.
- We mark an open circle at 2 and shade to the right of the open circle to represent x > 2.
So, the correct solution and graph for the inequality 2x - 2 < -12 or 2x + 3 > 7 is:
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.