Choose the correct solution and graph for the inequality.
2x-2-12 or 2x + 3 > 7
To solve the inequality 2x - 2 < -12, we will follow these steps:
Step 1: Add 2 to both sides of the inequality:
2x - 2 + 2 < -12 + 2
2x < -10
Step 2: Divide both sides of the inequality by 2 (since the coefficient of x is 2):
2x/2 < -10/2
x < -5
Therefore, the solution to the inequality 2x - 2 < -12 is x < -5.
To graph the solution on a number line, draw an open circle at -5 and shade the line to the left of -5.
Now let's solve the inequality 2x + 3 > 7:
Step 1: Subtract 3 from both sides of the inequality:
2x + 3 - 3 > 7 - 3
2x > 4
Step 2: Divide both sides of the inequality by 2 (since the coefficient of x is 2):
2x/2 > 4/2
x > 2
Therefore, the solution to the inequality 2x + 3 > 7 is x > 2.
To graph the solution on a number line, draw an open circle at 2 and shade the line to the right of 2.
To summarize, the correct solution is x < -5 OR x > 2.
The graph for this inequality would have an open circle at -5, a shaded line to the left of -5, an open circle at 2, and a shaded line to the right of 2.
To solve the inequality 2x - 2 - 12 < 2x + 3 > 7, we need to solve the two inequalities separately and then find their intersection.
First, let's solve the inequality 2x - 2 - 12 < 7:
Step 1: Combine like terms.
2x - 14 < 7
Step 2: Add 14 to both sides to isolate x.
2x < 21
Step 3: Divide both sides by 2 to solve for x.
x < 21/2 or x < 10.5
Now, let's solve the inequality 2x + 3 > 7:
Step 1: Subtract 3 from both sides.
2x > 4
Step 2: Divide both sides by 2 to solve for x.
x > 2
Since we have two inequalities, we need to find their intersection. In this case, the solution is the range of x values that satisfy both inequalities.
The solution is x < 10.5 and x > 2. Graphically, this can be represented by an open circle at x = 10.5 (since the inequality is strictly less than) and an open circle at x = 2 (since the inequality is strictly greater than). Then, shade the region between these two points to represent the values that satisfy both inequalities.
I hope this helps! Let me know if you have any further questions.
To find the solution and graph for the inequality 2x - 2 < -12 or 2x + 3 > 7, we can solve each inequality separately and then combine the solutions.
First, let's solve the inequality 2x - 2 < -12:
2x - 2 < -12
Add 2 to both sides to isolate the variable:
2x - 2 + 2 < -12 + 2
2x < -10
Divide both sides by 2 to solve for x:
2x/2 < -10/2
x < -5
Now, let's solve the inequality 2x + 3 > 7:
2x + 3 > 7
Subtract 3 from both sides to isolate the variable:
2x + 3 - 3 > 7 - 3
2x > 4
Divide both sides by 2 to solve for x:
2x/2 > 4/2
x > 2
Now we have the individual solutions:
x < -5 and x > 2
To graph these solutions on a number line, we can mark the points -5 and 2 on the number line and shade the regions based on the inequalities.
The region to the left of -5 (excluding -5) represents the solution for x < -5.
The region to the right of 2 (excluding 2) represents the solution for x > 2.
To graphically represent this on a number line, you would have an open circle at -5 and an open circle at 2, and then shade the regions to the left of -5 and to the right of 2.