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Chapter 3: Q66. (page 115)

Solve each equation. Check your solution.

66.6a-4=-2

Short Answer

Expert verified

There are no solutions to the equation 6a-4=-2. The solution set is 鈭�.

Step by step solution

01

Step-1 – Apply the concept of Absolute value

On real number line, the distance of a number from 0 is the absolute value. It is always nonnegative.

The absolute value of a function is expressed as, if x is a real number then absolute value of xis defined as.

x=x when x is greater than or equal to 0 . In other words, the absolute value of x is x when x is either positive or zero.

x=-x when x is less than 0 . In other words, the absolute value of x is opposite of x when x is negative.

02

Step-2 –Example of Absolute value

The absolute value of 5 is expressed as 5=5 and of -5 is expressed as -5=5

03

Step-3 – Simplify the equation

Consider the provided equation.

6a-4=-2

Recall that absolute value always produces a positive number. So, the equation is false.

No value exists for asuch that equation is true.

Hence, the solution set is 鈭�.

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