Linear Equations with Fractions and Decimals

Solving linear equations with fractions and decimals involves the same fundamental principles as solving linear equations with integers. The main goal is still to isolate the variable on one side of the equation. However, you might need to perform a few extra steps to handle the fractions or decimals effectively.

The following diagram gives example of solving linear equations with fractions or decimals. Scroll down the page for more examples and solutions of solving linear equations.

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Solving Linear Equations with Fractions

1. Identify all the denominators present in the equation and find the least common denominators (LCD).
2. Multiply both sides of the equation (and every individual term within the equation) by the LCD. This step will eliminate all the fractions.
3. After clearing the fractions, you’ll be left with a linear equation involving only integers. Solve this equation using the standard steps (combine like terms, isolate the variable).

Solving Linear Equations with Decimals

1. Look at all the decimal numbers in the equation and find the one with the greatest number of digits after the decimal point.
2. Multiply both sides of the equation (and every individual term) by a power of 10 that will shift the decimal point to the right enough to make all decimal numbers integers.
3. After clearing the decimals, you’ll have a linear equation with integers. Solve it using the standard steps.

Solving Equations with Fractions or Decimals
This video will review how to clear a linear equation in one variable of fractions or decimals.

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Linear equations with fractions
Example:
1/2 x + 1/4 = 3/8 x
2/3(x - 3) + 1/6 = 4

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Linear equations with fractions, decimals, addition property
Example:
1.1q = 2.7 - 2.5q
3/7 x + 1/4 = 1/3 - 4/7 x + 1/3

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Solve linear equation with decimals - clear decimals
Example:
0.20(24) + 0.05x = 0.10(6 + x)

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Linear equations with no solution or all real numbers

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