What does it mean to solve an equation, have the variables cancel out, and have the answer be 3=3,
To solve an equation means to find the values or solutions for the variables that make the equation true.
When the variables cancel out, it means that the equation simplifies in such a way that the variables on both sides of the equation disappear. This usually occurs when there are equal and opposite terms involving the variable on each side of the equation, causing them to "cancel out" when combined.
Having the answer be 3=3 means that both sides of the equation are equal to each other. In this case, it shows that the equation is true for any value of the variable because no matter what value is substituted for the variable, both sides of the equation will always be equal to 3.
What does it mean to solve an equation, have the variables cancel out, and have the answer be 3=3, For example?
One solution
Infinite solutions
No solutions
When solving an equation, there can be three possible outcomes:
1. One solution: This means that there is only one value for the variable that makes the equation true. The equation may have additional terms, but they all combine in a way that leaves only one possible solution. For example, if you solve the equation 2x + 3 = 9, you will find that x = 3, which is the only value that satisfies the equation.
2. Infinite solutions: This means that every value for the variable makes the equation true. In this case, the equation may simplify or have terms that cancel out, resulting in both sides being identical. For example, if you solve the equation x + 2 = x + 2, you will find that any value of x makes this equation true. So, it has infinite solutions.
3. No solutions: This means that there is no value for the variable that makes the equation true. When solving the equation, you may find that the variable cancels out or simplifies, but the resulting statement is false, such as 3 = 4. For example, if you solve the equation 2x + 5 = 2x + 10, you will find that the variable cancels out, but you end up with 5 = 10, which is not true. Therefore, there are no solutions to this equation.
What does it mean to solve an equation, have the variables cancel out, and have the answer be 3=3?
One solution
Infinite solutions
No solutions
When solving an equation, it means finding the value or values of the variable that make the equation true.
If the variables cancel out during the process of solving, it usually happens when there are equal and opposite terms involving the variable on each side of the equation, causing them to "cancel out" or eliminate each other.
If the answer is 3=3, it means that both sides of the equation are equal, which implies that the equation is true for any value of the variable. In this case, it indicates that there are infinite solutions to the equation, as any value substituted for the variable would satisfy the equation and make it true.
Sovle for x: 2x+4+3x=39
To solve for x in the equation 2x + 4 + 3x = 39, we need to combine like terms and isolate the variable on one side of the equation.
First, combine the x terms:
2x + 3x = 39 - 4
This simplifies to:
5x = 35
To isolate x, divide both sides of the equation by 5:
(5x)/5 = 35/5
This further simplifies to:
x = 7
Therefore, the solution to the equation 2x + 4 + 3x = 39 is x = 7.
What are the order of operations?
The order of operations, also known as the PEMDAS acronym, is a set of rules that dictates the sequence in which mathematical operations should be performed in an expression to result in a consistent and unambiguous solution. The order of operations is as follows:
1. Parentheses (or brackets): Perform operations inside parentheses or brackets first, starting from the innermost set and moving outward.
2. Exponents (or powers): Evaluate any exponentiation or power operations.
3. Multiplication and Division: Perform multiplication and division operations from left to right in the order they appear in the expression.
4. Addition and Subtraction: Perform addition and subtraction operations from left to right in the order they appear in the expression.
These rules ensure that mathematical expressions are evaluated in a standardized manner, preventing ambiguity and producing consistent results.