When solving linear equations the goal is to determine what value, if any, will solve the equation. A general guideline is to use the order of operations to simplify the expressions on both sides first.
Solve for x:
The solution set is
.
Conditional equations, identities, and contradictions
There are three different kinds of equations defined as follows.
Conditional Equation
A conditional equation is true for particular values of the variable.
Identity
An identity is an equation that is true for all possible values of the variable. For example, x = x has a solution set consisting of all real numbers,
.
Contradiction
A contradiction is an equation that is never true and thus has no solutions. For example, x + 1 = x has no solution. No solution can be expressed as the empty set
.
So far we have seen only conditional linear equations which had one value in the solution set. If when solving an equation and the end result is an identity, like say 0 = 0, then any value will solve the equation. If when solving an equation the end result is a contradiction, like say 0 = 1, then there is no solution.
Solve for x:
There is no solution,
.
Solve for y:
The equation is an identity, the solution set consists of all real numbers,
.
Linear literal equations
Literal equations, or formulas, usually have more than one variable. Since the letters are placeholders for values, the steps for solving them are the same. Use the properties of equality to isolate the indicated variable.
Solve for a:
Solution:
Solve for x:
Solution
Exercises
Checking solutions
Yes
No
Yes
Yes
No
Solving in one step
Solve in two steps
Solve in multiple steps
No Solution,
All Reals,
All Reals,
Literal equations
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature