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QuestionSolve the equation 3=−2∣14s−5∣+33=-2\left|\frac{1}{4} s-5\right|+3.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, and is always non-negative. . We need to find the value of ss that satisfies the equation 3=−∣14s−5∣+33=-\left|\frac{1}{4} s-5\right|+3.

STEP 2

First, let's simplify the equation by subtracting from both sides.
−=−2∣14s−5∣+− - = -2\left|\frac{1}{4} s-5\right|+ -

STEP 3

implify the left and right sides of the equation.
0=−2∣1s−5∣0 = -2\left|\frac{1}{} s-5\right|

STEP 4

Next, we can divide both sides of the equation by -2 to isolate the absolute value.
0−2=−2∣14s−∣−2\frac{0}{-2} = \frac{-2\left|\frac{1}{4} s-\right|}{-2}

STEP 5

implify the left and right sides of the equation.
0=∣14s−5∣0 = \left|\frac{1}{4} s-5\right|

STEP 6

The absolute value of a number is0 if and only if the number itself is0. So, we can remove the absolute value sign and set the expression inside equal to0.
14s−5=0\frac{1}{4} s-5 =0

STEP 7

Add5 to both sides of the equation to isolate the term with ss on one side.
14s−5+5=0+5\frac{1}{4} s-5 +5 =0 +5

STEP 8

implify the left and right sides of the equation.
14s=5\frac{1}{4} s =5

STEP 9

Multiply both sides of the equation by4 to solve for ss.
4⋅4s=4⋅54 \cdot \frac{}{4} s =4 \cdot5

STEP 10

implify the left and right sides of the equation.
s=20s =20The solution to the equation 3=−2∣4s−5∣+33=-2\left|\frac{}{4} s-5\right|+3 is s=20s =20.

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