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QuestionSolve the equation: ∣0.04x−1∣=6.04|0.04 x-1|=6.04

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of the direction.. Therefore, if ∣a∣=b|a| = b, then aa can be either bb or −b-b.

STEP 2

We can write two equations from the given absolute value equation, ∣0.04x−1∣=6.04|0.04x -1| =6.04, as follows0.04x−1=6.040.04x -1 =6.04and0.04x−1=−6.040.04x -1 = -6.04

STEP 3

Let's solve the first equation. Add1 to both sides to isolate the term with xx.
0.04x=6.04+10.04x =6.04 +1

STEP 4

Calculate the right side of the equation.
0.04x=7.040.04x =7.04

STEP 5

Now, divide both sides by 0.040.04 to solve for xx.
x=7.040.04x = \frac{7.04}{0.04}

STEP 6

Calculate the value of xx.
x=176x =176

STEP 7

Now, let's solve the second equation. Add1 to both sides to isolate the term with xx.
0.04x=−6.04+10.04x = -6.04 +1

STEP 8

Calculate the right side of the equation.
0.04x=−5.040.04x = -5.04

STEP 9

Now, divide both sides by .04.04 to solve for xx.
x=−5.04.04x = \frac{-5.04}{.04}

STEP 10

Calculate the value of xx.
x=−126x = -126So, the solutions to the equation ∣0.04x−∣=6.04|0.04x -| =6.04 are x=176x =176 and x=−126x = -126.

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