Question

Solve each equation. Check your solution.

$66.\left|6a-4\right|=-2$

Short answer

There are no solutions to the equation $\left|6a-4\right|=-2$. The solution set is $\varnothing$.

Step-by-step solution

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.

$\left|x\right|=x$ 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.

$\left|x\right|=-x$ when x is less than 0 . In other words, the absolute value of x is opposite of x when x is negative.

Step-2 –Example of Absolute value

The absolute value of 5 is expressed as $\left|5\right|=5$ and of $-5$ is expressed as $\left|-5\right|=5$

Step-3 – Simplify the equation

Consider the provided equation.

$\left|6a-4\right|=-2$

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 $\varnothing$.