How can you solve an equation or inequality in one variable?
huh. That's quite a question just to drop in. Have you not studied your algebra text?
The basic idea is that if an equation is true, it remains true if you apply identical operations on both sides of the equal sign.
The goal is to choose the operations in an order which will isolate the variable by itself on one side of the equation. Then you have solved the equation.
For example, if the equation is
3x+9 = 30
You want x all by itself. So, get rid of the +9 by doing "-9" on both sides:
3x+9-9 = 30-9
3x = 21
Now you have all the x stuff on one side, but you still don't have x b y itself. Since 3/3=1, divide both sides by 3:
3x/3 = 21/3
x = 7
Now you are done. If you substitute 7 in for x in the original equation, it will be true:
3(7)+9 = 30
21+9 = 30
30 = 30
To solve an equation or inequality in one variable, such as x, you can follow these general steps:
1. Isolate the variable: Move all terms containing the variable to one side of the equation or inequality. This typically involves performing arithmetic operations such as addition, subtraction, multiplication, and division on both sides.
2. Simplify the equation or inequality: Combine like terms and perform any necessary simplifications.
3. Solve for the variable: Further manipulate the equation or inequality to get the variable alone on one side. This will give you the solution(s).
4. Check your answer: Plug the solution(s) back into the original equation or inequality to verify that it satisfies the given conditions.
Let's illustrate these steps with an example:
Example 1: Solve the equation 2x - 5 = 7.
Step 1: Isolate the variable.
We'll move the constant term (-5) to the right side by adding 5 to both sides:
2x - 5 + 5 = 7 + 5,
which simplifies to:
2x = 12.
Step 2: Simplify the equation.
Since there is no further simplification, we move to the next step.
Step 3: Solve for the variable.
To isolate x, we divide both sides by 2:
2x/2 = 12/2,
resulting in:
x = 6.
Step 4: Check the answer.
We substitute x = 6 back into the original equation:
2(6) - 5 = 7,
which simplifies to:
12 - 5 = 7,
showing that the solution x = 6 satisfies the equation.
Remember, when solving inequalities, the steps are similar, but with one key difference: if you multiply or divide both sides by a negative number, you must reverse the inequality symbol.
I hope this explanation helps you solve equations and inequalities in one variable successfully!