{"id":249225,"date":"2024-04-23T21:08:14","date_gmt":"2024-04-23T21:08:14","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=249225"},"modified":"2024-04-23T21:08:14","modified_gmt":"2024-04-23T21:08:14","slug":"how-do-you-solve-absolute-value-equations-with-fractions-2","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-absolute-value-equations-with-fractions-2\/","title":{"rendered":"How do you solve absolute value equations with fractions?"},"content":{"rendered":"

How do you solve absolute value equations with fractions?<\/p>\n

Solving absolute value equations with fractions requires understanding the properties of absolute value and applying them to the given equation. Here is a step-by-step guide on how to solve such equations:<\/p>\n

Step 1: Set up the equation<\/p>\n

Begin by writing the given absolute value equation. For example, consider the equation |(x\/2) – 3| = 4\/5.<\/p>\n

Step 2: Isolate the absolute value expression<\/p>\n

To isolate the absolute value expression, we need to get rid of the absolute value bars. We do this by separating the equation into two separate equations: one with the positive of the expression inside the absolute value and the other with the negative of the expression.<\/p>\n

In the above example,
\n(x\/2) – 3 = 4\/5 and (x\/2) – 3 = -4\/5<\/p>\n

Step 3: Solve each equation separately<\/p>\n

Solve each equation separately to find the possible values of the variable.<\/p>\n

For the equation (x\/2) – 3 = 4\/5,<\/p>\n

Add 3 to both sides to isolate the variable:
\n(x\/2) = 4\/5 + 3<\/p>\n

Now, find a common denominator (in this case, it is 5) and add the fractions:
\n(x\/2) = 4\/5 + 15\/5<\/p>\n

Simplify the right side of the equation:
\n(x\/2) = 19\/5<\/p>\n

Multiply both sides of the equation by 2 to solve for x:
\nx = 19\/5 * 2<\/p>\n

Simplify:
\nx = 38\/5<\/p>\n

Similarly, for the equation (x\/2) – 3 = -4\/5,<\/p>\n

Add 3 to both sides:
\n(x\/2) = -4\/5 + 3<\/p>\n

Find a common denominator and add the fractions:
\n(x\/2) = -4\/5 + 15\/5<\/p>\n

Simplify:
\n(x\/2) = 11\/5<\/p>\n

Multiply both sides by 2 to solve for x:
\nx = 11\/5 * 2<\/p>\n

Simplify:
\nx = 22\/5<\/p>\n

Therefore, the solutions to the absolute value equation |(x\/2) – 3| = 4\/5 are x = 38\/5 and x = 22\/5.<\/p>\n

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