Questions and Answers
Solve for x in the equation x + 2 = 9.
x = 7
Solve for x in the equation 3x - 4 = 14.
x = 6
Solve for x in the equation 2x = 16.
x = 8
Solve for x in the equation x - 2 = 5.
Signup and view all the answers
Solve for x in the equation 4x + 2 = 18.
Signup and view all the answers
Solve for x in the equation x + 1 = 3x - 2.
Signup and view all the answers
Solve for x in the equation 2x - 3 = 7.
Signup and view all the answers
Solve for x in the equation x/2 + 2 = 5.
Signup and view all the answers
Study Notes
Solving Linear Equations
Definition
- A linear equation in one variable is an equation that can be written in the form: ax + b = 0, where a and b are constants, and x is the variable.
Steps to Solve Linear Equations
- Simplify the equation: Combine like terms and eliminate any parentheses.
- Isolate the variable: Use addition, subtraction, multiplication, or division to isolate the variable (x) on one side of the equation.
- Check the solution: Plug the solution back into the original equation to ensure it is true.
Types of Linear Equations
- Simple equations: Equations that can be solved in one step, such as 2x = 6.
- Multi-step equations: Equations that require more than one step to solve, such as 2x + 3 = 7.
- Equations with variables on both sides: Equations where the variable appears on both sides, such as 2x + 3 = x + 5.
Solving Linear Equations with Special Cases
- Zero on one side: If the equation has zero on one side, such as 2x + 3 = 0, solve for x by adding or subtracting the same value to both sides.
- Variables with coefficients: If the equation has variables with coefficients, such as 2x + 3 = 4x - 2, solve for x by adding or subtracting the same value to both sides, and then dividing both sides by the coefficient.
Common Errors to Avoid
- Forgetting to check the solution: Always plug the solution back into the original equation to ensure it is true.
- Incorrectly isolating the variable: Be careful when adding, subtracting, multiplying, or dividing both sides of the equation to avoid introducing errors.
Solving Linear Equations
Definition
- A linear equation in one variable is an equation that can be written in the form: ax + b = 0, where a and b are constants, and x is the variable.
Steps to Solve Linear Equations
- Simplify the equation by combining like terms and eliminating any parentheses.
- Isolate the variable by using addition, subtraction, multiplication, or division to get the variable (x) on one side of the equation.
- Check the solution by plugging it back into the original equation to ensure it is true.
Types of Linear Equations
- Simple equations are equations that can be solved in one step, such as 2x = 6.
- Multi-step equations require more than one step to solve, such as 2x + 3 = 7.
- Equations with variables on both sides are equations where the variable appears on both sides, such as 2x + 3 = x + 5.
Solving Linear Equations with Special Cases
- If the equation has zero on one side, such as 2x + 3 = 0, solve for x by adding or subtracting the same value to both sides.
- If the equation has variables with coefficients, such as 2x + 3 = 4x - 2, solve for x by adding or subtracting the same value to both sides, and then dividing both sides by the coefficient.
Common Errors to Avoid
- Always check the solution by plugging it back into the original equation to ensure it is true.
- Be careful when adding, subtracting, multiplying, or dividing both sides of the equation to avoid incorrectly isolating the variable.
Solving Linear Equations
- A linear equation in one variable can be written in the form
ax + b = 0, whereaandbare constants anda ≠ 0. - The goal is to solve for
x, finding the value ofxthat makes the equation true.
Steps to Solve Linear Equations
- Simplify the equation by combining like terms on each side of the equation, if possible.
- Isolate the variable
xusing addition, subtraction, multiplication, or division to getxalone on one side of the equation. - Check the solution by plugging it back into the original equation to verify it is true.
Find x type question
- These types of questions ask to solve for
xin a linear equation. - Examples of
Find xtype questions include2x + 5 = 11,x - 3 = 7, and4x = 24.
Solving Strategies
- Use addition or subtraction to get rid of constants in an equation.
- Use multiplication or division to get rid of coefficients in an equation.
- Use inverse operations to isolate
x, such as using-to get rid of+and vice versa.
Examples with Solutions
-
2x + 5 = 11can be solved by subtracting 5 from both sides, resulting in2x = 6, and then dividing both sides by 2, resulting inx = 3. -
x - 3 = 7can be solved by adding 3 to both sides, resulting inx = 10.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn how to solve linear equations in one variable, including simplifying the equation, isolating the variable, and checking the solution.
