What does it mean to solve an equation, have the variables cancel out, and have the answer be 3=3, for example?
*
1 point
one solution
infinite solutions
no solution
When solving an equation, the goal is to find the value(s) of the variable(s) that make the equation true. If the variables cancel out during the solving process and the resulting equation is true, such as 3=3, it means that the equation is always true regardless of the value of the variable. This indicates that the original equation has infinite solutions.
Solve for x: 2x + 4 + 3x = 39
*
1 point
x = 13
x = 7
x = 39
To solve for x in the equation 2x + 4 + 3x = 39, you first combine like terms on the left side of the equation:
2x + 3x + 4 = 39
5x + 4 = 39
Next, you isolate the variable x by subtracting 4 from both sides of the equation:
5x + 4 - 4 = 39 - 4
5x = 35
To solve for x, divide both sides of the equation by 5:
(5x)/5 = 35/5
x = 7
Therefore, the correct answer is x = 7.
What are the order of operations?
The order of operations is a set of rules that determines the sequence in which mathematical operations should be performed in an expression or equation. The order of operations is commonly remembered with the acronym PEMDAS, which stands for:
1. Parentheses: Perform calculations inside parentheses first.
2. Exponents: Evaluate any exponential operations.
3. Multiplication and Division: Perform these operations from left to right.
4. Addition and Subtraction: Perform these operations from left to right.
Following the order of operations ensures that the expression or equation is evaluated correctly and consistently.
What are the order of operations?
*
6 points
Parenthesis Multiplication Addition Division Exponents Subtraction
1st step
2nd step
3rd step
4th step
5th step
6th step
1st step
2nd step
3rd step
4th step
5th step
6th step
The correct order of operations is as follows:
1st step: Parentheses (Perform calculations inside parentheses first)
2nd step: Exponents (Evaluate any exponential operations)
3rd step: Multiplication and Division (Perform these operations from left to right)
4th step: Addition and Subtraction (Perform these operations from left to right)
So the correct order of operations is:
1st step: Parentheses
2nd step: Exponents
3rd step: Multiplication and Division
4th step: Addition and Subtraction
If there is no number before a variable, is there a coefficient and what would it be?
*
1 point
0
1
If there is no number before a variable, it is considered to have a coefficient of 1. In algebraic terms, the coefficient is the number that is multiplied by the variable. So if there is no number explicitly written before a variable, it is understood to be 1.
Solve the equation: 6(x-2) -2x = 4x
*
1 point
x= -12
x = 0
-12=0 no solution