{"id":249275,"date":"2024-05-06T10:22:30","date_gmt":"2024-05-06T10:22:30","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=249275"},"modified":"2024-05-06T10:22:30","modified_gmt":"2024-05-06T10:22:30","slug":"how-do-you-solve-an-absolute-value-equation-with-fractions-2","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-an-absolute-value-equation-with-fractions-2\/","title":{"rendered":"How do you solve an absolute value equation with fractions?"},"content":{"rendered":"

Absolute value equations can be challenging to solve, especially when fractions are involved. However, with a systematic approach and a few key steps, you can successfully solve these equations and find the correct solutions. In this article, we will walk you through the process of solving an absolute value equation with fractions.<\/p>\n

How do you solve an absolute value equation with fractions?<\/b><\/p>\n

To solve an absolute value equation with fractions, follow these steps:<\/p>\n

1. Begin by isolating the absolute value on one side of the equation. If necessary, distribute any denominators to clear the fractions.
\n2. Next, remove the absolute value bars by splitting the equation into two separate equations: one with a positive value inside the absolute value bars and the other with a negative value inside the absolute value bars.
\n3. Solve each equation separately by isolating the variable.
\n4. Once you have found the two potential solutions, simplify them if needed by canceling out any common factors or reducing fractions.<\/p>\n

Let’s explain the process with an example equation: |(2x – 1)\/3| = 5\/4.<\/p>\n

Step 1: Isolate the absolute value.
\n(2x – 1)\/3 = 5\/4<\/p>\n

Step 2: Remove the absolute value bars.
\n(2x – 1)\/3 = 5\/4 OR (2x – 1)\/3 = -5\/4<\/p>\n

Step 3: Solve each equation separately.
\nFor the first equation:
\n2x – 1 = 15\/4
\n2x = 15\/4 + 1
\n2x = 15\/4 + 4\/4
\n2x = 19\/4
\nx = 19\/8<\/p>\n

For the second equation:
\n2x – 1 = -15\/4
\n2x = -15\/4 + 1
\n2x = -15\/4 + 4\/4
\n2x = -11\/4
\nx = -11\/8<\/p>\n

Step 4: Simplify the solutions.
\nx = 19\/8 simplifies to x = 2.375
\nx = -11\/8 simplifies to x = -1.375<\/p>\n

Therefore, the solutions to the absolute value equation |(2x – 1)\/3| = 5\/4 are x = 2.375 and x = -1.375.<\/p>\n

\n
\n

Table of Contents<\/p>\nToggle<\/span><\/path><\/svg><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n