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QuestionSolve the equation −1.8(z−18)=1.8(z−1.5)-1.8(z-18)=1.8(z-1.5) and express the answer as an integer, fraction, or decimal (2 decimal places).

Studdy Solution

STEP 1

Assumptions1. The equation is linear and in the form -1.8(z-18)=1.8(z-1.5) . We are to solve for the variable z3. The solution should be expressed as an integer, a simplified fraction, or a decimal rounded to two decimal places

STEP 2

First, we need to distribute the -1.8 on the left side of the equation and the1.8 on the right side of the equation.
−1.8z+32.4=1.8z−2.7-1.8z +32.4 =1.8z -2.7

STEP 3

Now, we can add1.8z to both sides of the equation to get all the z terms on one side.
−1.8z+1.8z+32.=1.8z−2.7+1.8z-1.8z +1.8z +32. =1.8z -2.7 +1.8z

STEP 4

implify the equation.
32.4=3.6z−2.732.4 =3.6z -2.7

STEP 5

Next, we add2.7 to both sides of the equation to isolate the z term.
32.4+2.7=3.z−2.7+2.732.4 +2.7 =3.z -2.7 +2.7

STEP 6

implify the equation.
35.1=3.6z35.1 =3.6z

STEP 7

Finally, we divide both sides of the equation by3.6 to solve for z.
z=35.13.6z = \frac{35.1}{3.6}

STEP 8

Calculate the value of z.
z=35.13.6≈.75z = \frac{35.1}{3.6} \approx.75The solution to the equation is z =.75.

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