A. "Solve for w: (6w+1)/5≠2. Describe the solution in set notation."
First I must find what number to substitute for "w" that WILL equal 2, correct? Then, determine the numbers that won't (I assume there will be far more of these)? What would be the most efficient way to go about this?
I'm also really struggling with this concept of writing equations that are always or almost always true. If I could receive some advice on how to tackle these sorts of problems, that would be helpful.
Thank you very much for the assistance. :-)
Take care!
You can solve it like almost any equation, but replacing the equality sign with \≠.
For example,
solve for q in (4a+3)/5≠3
so we can continue
4a+3≠5*3
4a≠15-3
4a≠12
a≠3 is the answer.
In set notation,
a ∈ R\3, or
a ∈ (-∞,3)∪(3,∞)
(Remember: this is an example)
To solve the equation (6w+1)/5 ≠ 2, we need to find the values of w that make the equation true. The inequality sign "≠" indicates that we are looking for values of w that are not equal to 2.
To find these values, we can start by isolating w in the equation. First, multiply both sides of the equation by 5 to get rid of the denominator:
(6w+1)/5 ≠ 2
5 * (6w+1)/5 ≠ 5 * 2
6w+1 ≠ 10
Next, subtract 1 from both sides of the equation to isolate 6w:
6w+1 - 1 ≠ 10 - 1
6w ≠ 9
Now, divide both sides of the equation by 6 to solve for w:
6w/6 ≠ 9/6
w ≠ 3/2
So, the solution for w is any value that is not equal to 3/2 or 1.5.
In set notation, this can be expressed as:
w ∈ ℝ, w ≠ 3/2
This means that w belongs to the set of all real numbers, except for 3/2.
Regarding your question about writing equations that are always or almost always true, these are called identities or conditional equations. An identity is an equation that holds true for all possible values of the variable, while a conditional equation is an equation that holds true for certain values of the variable, which you need to determine.
To approach these problems, it's important to have a good understanding of algebraic properties and rules. You can start by simplifying both sides of the equation and see if they can be transformed into equal expressions. If you reach the same expression on both sides, then it is an identity. If not, you may need to manipulate the equation further or find specific values that satisfy the equation.
Practicing different types of equations and inequalities will help you gain familiarity and develop strategies to solve them efficiently. Don't hesitate to ask for clarification or seek additional resources when needed.