Directions:Solve and graph the inequality using words.
Problem:
1.)2x>-4 and x-4<=2
2.)x+3=>2x+1 and -4x<-8
3.)-6<x+3>6(Remember this is an "and" statement)
this doesn't look like a question.
You're right, these are not questions but rather inequalities that need to be solved and graphed. Let's break down each problem step by step:
1.) 2x > -4 and x - 4 <= 2:
To solve and graph this inequality, we need to break it down into two separate inequalities and then find the common solution.
First inequality: 2x > -4
To solve for x, we divide both sides by 2: x > -2
Second inequality: x - 4 <= 2
To solve for x, we add 4 to both sides: x <= 6
Now, we look for the common solution. Since the original problem is an "and" statement, we need to find the values of x that satisfy both x > -2 and x <= 6. By graphing these two inequalities on a number line, we can determine the overlapping region, which represents the common solution set.
2.) x + 3 >= 2x + 1 and -4x < -8:
Again, let's break down this inequality into two separate inequalities.
First inequality: x + 3 >= 2x + 1
To solve for x, we subtract x from both sides: 3 >= x + 1
Then, subtract 1 from both sides: 2 >= x
Second inequality: -4x < -8
To solve for x, we divide both sides by -4. Remember, when dividing or multiplying by a negative number, we need to reverse the inequality symbol: x > 2
Now, let's find the common solution. Since the original problem is an "and" statement, we need to find the values of x that satisfy both 2 >= x and x > 2. By graphing these two inequalities on a number line, we can determine that there is no overlapping region, which means there is no common solution.
3.) -6 < x + 3 > 6:
Similar to the previous examples, we need to break down this inequality as well.
First inequality: -6 < x + 3
To solve for x, we subtract 3 from both sides: -9 < x
Second inequality: x + 3 > 6
To solve for x, we subtract 3 from both sides: x > 3
Now, let's find the common solution. Since the original problem is an "and" statement, we need to find the values of x that satisfy both -9 < x and x > 3. By graphing these two inequalities on a number line, we can determine that there is no overlapping region, which means there is no common solution.
In summary, for the first problem, the common solution is x > -2 and x <= 6. For the second problem, there is no common solution. And for the third problem, there is no common solution either.