First-Degree+Equations


 * First-Degree Equations: An equation that has only one variable, and each instance of the variable is to the first power. **

**Solving Equations**

Linear equations are also called first degree equations, as the highest power of the variable (algebraic expressions/pronumeral) in these equations is 1. E.g. //x// + 5 = 9 is an equation of the first degree, which is often called a linear equation. Many problems can be solved by using linear equations. Equations behave like a balance. So we need to apply the same **operation** to both sides of an equation to maintain the balance. This means we can:
 * add the same number to both sides of an equation
 * subtract the same number from both sides of an equation
 * multiply both sides of an equation by the same number
 * divide both sides of an equation by the same number

Equations
An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers. Many word problems can easily be written down as equations with a little practice. Many simple rules exist for simplifying equations. Example: The following are examples of equations: 2 = 2 17 = 2 + 15 //x// = 7 7 = //x// //t// + 3 = 8 3 × //n// +12 = 100 //w// + 4 = 12 - //w// //y// - 1 - 2 - 9.3 = 34 3 × (//d// + 4) - 11 = 321 - 23 Example: Translate the following word problem into an equation: My age in years //y// plus 20 is equal to four times my age, minus 10. The first expression stands for "my age in years plus 20", which is //y// + 20. This is equal to the second expression for "four times my age, minus 10", which is 4 × //y// - 10. Setting these two expressions equal to one another gives us the equation: //y// + 20 = 4 × //y// - 10

Solution of an Equation
When an equation has a variable, the solution to the equation is the number that makes the equation true when we replace the variable with its value. Example: We say //y// = 3 is a solution to the equation 4 × //y// + 7 = 19, for replacing each occurrence of //y// with 3 gives us 4 × 3 + 7 = 19 ==> 12 + 7 = 19 ==> 19 = 19 which is true. Examples: //x// = 100 is a solution to the equation //x// ÷ 2 - 40 = 10 //z// = 12 is a solution to the equation 5 × (//z// - 6) = 30 Counterexample: //y// = 10 is NOT a solution to the equation 4 × //y// + 7 = 19. When we replace each //y// with 10, we get 4 × 10 + 7 = 19 ==> 40 + 7 = 19 ==> 47 = 19 not true! Counterexamples: //x// = 200 is NOT a solution to the equation //x// ÷ 2 - 40 = 10 //z// = 20 is NOT a solution to the equation 5 × (//z// - 6) = 30