Decimals
Because decimal numbers are fractions in disguise, the same trick can be used to ‘‘clear the decimal’’ in equations with decimal numbers. Count the largest number of digits behind each decimal point and multiply both sides of the equation by 10 raised to the power of that number.
Alfi Blog Maret 01, 2026 Admin Bandung IndonesiaDecimals
Because decimal numbers are fractions in disguise, the same trick can be used to ‘‘clear the decimal’’ in equations with decimal numbers. Count the largest number of digits behind each decimal point and multiply both sides of the equation by 10 raised to the power of that number.
When the equation you are given has fractions and you prefer not to work with fractions, you can clear the fractions in the first step. Of course, the solution might be a fraction, but that fraction will not occur until the last step. Find the LCD of all fractions and multiply both sides of the equation by this number. Then, distribute this quantity on each side of the equation.
Alfi Blog Februari 28, 2026 Admin Bandung IndonesiaWhen the equation you are given has fractions and you prefer not to work with fractions, you can clear the fractions in the first step. Of course, the solution might be a fraction, but that fraction will not occur until the last step. Find the LCD of all fractions and multiply both sides of the equation by this number. Then, distribute this quantity on each side of the equation.
Some equations can be solved in a number of ways. However, the general method in this book will be the same:
Alfi Blog Februari 27, 2026 Admin Bandung IndonesiaSome equations can be solved in a number of ways. However, the general method in this book will be the same:
To solve equations for the unknown, use inverse operations to isolate the variable. These inverse operations ‘‘undo’’ what has been done to the variable. That is, inverse operations are used to move quantities across the equal sign. For instance, in the equation 5x = 10, x is multiplied by 5, so to move 5 across the equal sign, you need to ‘‘unmultiply’’ the 5. That is, divide both sides of the equation by 5 (equivalently, multiply each side of the equation by 1/5). In the equation 5 + x = 10, to move 5 across the equal sign, you must ‘‘unadd’’ 5. That is, subtract 5 from both sides of the equation (equivalently, add –5 to both sides of the equation).
Alfi Blog Februari 26, 2026 Admin Bandung IndonesiaTo solve equations for the unknown, use inverse operations to isolate the variable. These inverse operations ‘‘undo’’ what has been done to the variable. That is, inverse operations are used to move quantities across the equal sign. For instance, in the equation 5x = 10, x is multiplied by 5, so to move 5 across the equal sign, you need to ‘‘unmultiply’’ the 5. That is, divide both sides of the equation by 5 (equivalently, multiply each side of the equation by 1/5). In the equation 5 + x = 10, to move 5 across the equal sign, you must ‘‘unadd’’ 5. That is, subtract 5 from both sides of the equation (equivalently, add –5 to both sides of the equation).
Linear Equations
Now we can use the tools we have developed to solve equations. Up to now, we have rewritten expressions and added fractions. This chapter is mostly concerned with linear equations. In a linear equation, the variables are raised to the first power—there are no variables in denominators, no variables to any power (other than one), and no variables under root signs.
Alfi Blog Februari 25, 2026 Admin Bandung IndonesiaLinear Equations
Now we can use the tools we have developed to solve equations. Up to now, we have rewritten expressions and added fractions. This chapter is mostly concerned with linear equations. In a linear equation, the variables are raised to the first power—there are no variables in denominators, no variables to any power (other than one), and no variables under root signs.
