Solve
3x +1 < 5 or 3x +1 > 4
By saying "solve," is it asking for me to show it on a line and in interval notation?
Here's another:
f(x) < 3 and f(x) > 4, where f(x) = 1/2x - 7
I have no idea how to solve this! Please walk me through it!
Thank you so much!
I will do one.
The second..
1/2 x-7<3
1/2 x<10
x<20
1/2 x-7>4
1/2 x >11
x>22
so here x is less than 20 or greater than 22
To solve the inequalities, let's break it down step by step:
1. Solve inequality 3x + 1 < 5:
Subtract 1 from both sides: 3x < 4
Divide both sides by 3: x < 4/3
2. Solve inequality 3x + 1 > 4:
Subtract 1 from both sides: 3x > 3
Divide both sides by 3: x > 1
So, the solution to the first inequality is x < 4/3 or x > 1.
Now let's move on to the second problem:
1. Given: f(x) < 3 and f(x) > 4, where f(x) = (1/2)x - 7
We need to find the values of x that satisfy both inequalities. Let's solve them one by one:
2. Solve f(x) < 3:
Substitute f(x) = (1/2)x - 7: (1/2)x - 7 < 3
Add 7 to both sides: (1/2)x < 10
Multiply both sides by 2 (to eliminate the fraction): x < 20
3. Solve f(x) > 4:
Substitute f(x) = (1/2)x - 7: (1/2)x - 7 > 4
Add 7 to both sides: (1/2)x > 11
Multiply both sides by 2: x > 22
So, the solution to the second inequality is x < 20 and x > 22.
In summary, the solution to the combined inequalities f(x) < 3 and f(x) > 4 is x < 20 or x > 22.
Please note that when solving inequalities involving fractions or expressions with variables, it's important to pay attention to possible restrictions or values that may make the denominator equal to zero. In this case, there were no such restrictions.