Solving Linear Equations
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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.

<p><code>x = 7</code></p> Signup and view all the answers

Solve for x in the equation 4x + 2 = 18.

<p><code>x = 4</code></p> Signup and view all the answers

Solve for x in the equation x + 1 = 3x - 2.

<p><code>x = 3</code></p> Signup and view all the answers

Solve for x in the equation 2x - 3 = 7.

<p><code>x = 5</code></p> Signup and view all the answers

Solve for x in the equation x/2 + 2 = 5.

<p><code>x = 6</code></p> 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

  1. Simplify the equation: Combine like terms and eliminate any parentheses.
  2. Isolate the variable: Use addition, subtraction, multiplication, or division to isolate the variable (x) on one side of the equation.
  3. 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, where a and b are constants and a ≠ 0.
  • The goal is to solve for x, finding the value of x that 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 x using addition, subtraction, multiplication, or division to get x alone 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 x in a linear equation.
  • Examples of Find x type questions include 2x + 5 = 11, x - 3 = 7, and 4x = 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 = 11 can be solved by subtracting 5 from both sides, resulting in 2x = 6, and then dividing both sides by 2, resulting in x = 3.
  • x - 3 = 7 can be solved by adding 3 to both sides, resulting in x = 10.

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Description

Learn how to solve linear equations in one variable, including simplifying the equation, isolating the variable, and checking the solution.

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