{"id":214617,"date":"2024-03-24T22:06:55","date_gmt":"2024-03-24T22:06:55","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-absolute-value-with-fractions\/"},"modified":"2024-03-24T22:06:55","modified_gmt":"2024-03-24T22:06:55","slug":"how-do-you-solve-absolute-value-with-fractions","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-absolute-value-with-fractions\/","title":{"rendered":"How do you solve absolute value with fractions?"},"content":{"rendered":"

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

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. When dealing with fractions and absolute value, it is important to remember a few key steps to solve these equations accurately.<\/p>\n

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

1. Identify the given absolute value expression or equation.
\n2. If the absolute value is inside parentheses, first remove the parentheses.
\n3. Evaluate the expression within the absolute value, treating the fraction as a whole number.
\n4. Consider both the positive and negative results when evaluating the fraction inside the absolute value.
\n5. Simplify the absolute value expression or equation using the absolute value definition:<\/p>\n

– If the fraction inside the absolute value is positive or zero, the absolute value is equal to the fraction itself.
\n – If the fraction inside the absolute value is negative, the absolute value is equal to the opposite of the fraction.<\/p>\n

6. Replace the absolute value expression or equation with the simplified value obtained in step 5.
\n7. Solve the resulting equation or expression for the variable.<\/p>\n

To illustrate this process, let’s consider an example:<\/p>\n

Example 1: Solve the absolute value equation |2\/3x – 1| = 4\/3.<\/p>\n

Step 1: The given equation is |2\/3x – 1| = 4\/3.<\/p>\n

Step 2: Since there are no parentheses, we can proceed to evaluate the expression.<\/p>\n

Step 3: Consider both positive and negative results when evaluating the fraction inside the absolute value:
\n – When 2\/3x – 1 is positive or zero: 2\/3x – 1 = 4\/3.
\n – When 2\/3x – 1 is negative: -(2\/3x – 1) = 4\/3.<\/p>\n

Step 4: Now, solve each equation separately.<\/p>\n

– Case 1: 2\/3x – 1 = 4\/3.
\n Add 1 to both sides: 2\/3x = 4\/3 + 1\/1.
\n Simplify: 2\/3x = 4\/3 + 3\/3.
\n Combine fractions: 2\/3x = 7\/3.
\n Multiply both sides by 3\/2: x = (7\/3) * (3\/2).
\n Simplify: x = 7\/2.<\/p>\n

– Case 2: -(2\/3x – 1) = 4\/3.
\n Multiply both sides by -1 to eliminate the negative sign: 2\/3x – 1 = -4\/3.
\n Add 1 to both sides: 2\/3x = -4\/3 + 1\/1.
\n Simplify: 2\/3x = -4\/3 + 3\/3.
\n Combine fractions: 2\/3x = -1\/3.
\n Multiply both sides by 3\/2: x = (-1\/3) * (3\/2).
\n Simplify: x = -1\/2.<\/p>\n

Step 5: The solutions of the equation are x = 7\/2 and x = -1\/2.<\/p>\n

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