{"id":214652,"date":"2024-03-07T15:01:17","date_gmt":"2024-03-07T15:01:17","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-an-absolute-value-with-a-fraction\/"},"modified":"2024-03-07T15:01:17","modified_gmt":"2024-03-07T15:01:17","slug":"how-do-you-solve-an-absolute-value-with-a-fraction","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-an-absolute-value-with-a-fraction\/","title":{"rendered":"How do you solve an absolute value with a fraction?"},"content":{"rendered":"

How do you solve an absolute value with a fraction?<\/p>\n

When working with absolute values, it is common to encounter fractions. The process of solving an absolute value with a fraction involves understanding the concept of absolute value and applying appropriate operations to determine the solution. Let’s dive deeper into solving absolute values with fractions and address some related frequently asked questions.<\/p>\n

Absolute value, denoted by || surrounding a number or expression, simply gives the positive magnitude or value of a number. Therefore, |x| is equal to x when x is positive or zero, and -x when x is negative. When dealing with absolute values that contain fractions, the steps to solve them can be broken down into three parts:<\/p>\n

1. Determine the expression inside the absolute value.
\n2. Solve the expression as an equation, considering both the positive and negative versions of the fraction.
\n3. Use the positive and negative solutions obtained to represent the possible values of the absolute value.<\/p>\n

To illustrate this process, let’s consider an example: |(3\/4)x – 2| = 5\/6.<\/p>\n

First, we isolate the absolute value expression by removing the absolute value brackets: (3\/4)x – 2 = 5\/6 and -(3\/4)x + 2 = 5\/6.<\/p>\n

Now, we solve both equations individually.<\/p>\n

1. Solving (3\/4)x – 2 = 5\/6:
\n Add 2 to both sides: (3\/4)x = 5\/6 + 2
\n Simplify: (3\/4)x = 17\/6
\n Multiply both sides by (4\/3) to isolate x: x = (17\/6) * (4\/3)
\n Simplify: x = 68\/18 = 34\/9<\/p>\n

2. Solving -(3\/4)x + 2 = 5\/6:
\n Subtract 2 from both sides: -(3\/4)x = 5\/6 – 2
\n Simplify: -(3\/4)x = -7\/6
\n Multiply both sides by (-4\/3) to isolate x: x = (-7\/6) * (-4\/3)
\n Simplify: x = 28\/18 = 14\/9<\/p>\n

Now that we have obtained two possible solutions for x, we can represent the absolute value equation as two separate equations and solve for x:<\/p>\n

1. (3\/4)x – 2 = 5\/6:
\n Add 2 to both sides: (3\/4)x = 5\/6 + 2
\n Simplify: (3\/4)x = 17\/6
\n Multiply both sides by (4\/3) to isolate x: x = (17\/6) * (4\/3)
\n Simplify: x = 68\/18 = 34\/9<\/p>\n

2. -(3\/4)x + 2 = 5\/6:
\n Subtract 2 from both sides: -(3\/4)x = 5\/6 – 2
\n Simplify: -(3\/4)x = -7\/6
\n Multiply both sides by (-4\/3) to isolate x: x = (-7\/6) * (-4\/3)
\n Simplify: x = 28\/18 = 14\/9<\/p>\n

Therefore, the solutions to the absolute value equation |(3\/4)x – 2| = 5\/6 are x = 34\/9 and x = 14\/9.<\/p>\n

\n
\n

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