Answer :

GinnyAnswer
Certainly! Let's solve the equation step-by-step:

Given:
[tex]\[ \frac{0.4z - 3}{1.5z + 9} = \frac{7}{5} \][/tex]

Step 1: Cross-Multiply to Eliminate the Fractions

To eliminate the fractions, we can cross-multiply:
[tex]\[ 5(0.4z - 3) = 7(1.5z + 9) \][/tex]

Step 2: Distribute the Constants on Both Sides

Distribute 5 on the left side and 7 on the right side:
[tex]\[ 5 \times 0.4z - 5 \times 3 = 7 \times 1.5z + 7 \times 9 \][/tex]
[tex]\[ 2z - 15 = 10.5z + 63 \][/tex]

Step 3: Move All Terms Involving [tex]\(z\)[/tex] to One Side

Subtract [tex]\(10.5z\)[/tex] from both sides to get all [tex]\(z\)[/tex]-terms on one side:
[tex]\[ 2z - 10.5z - 15 = 63 \][/tex]
[tex]\[ -8.5z - 15 = 63 \][/tex]

Step 4: Isolate the [tex]\(z\)[/tex]-Term

Add 15 to both sides to move the constant term to the right:
[tex]\[ -8.5z = 63 + 15 \][/tex]
[tex]\[ -8.5z = 78 \][/tex]

Step 5: Solve for [tex]\(z\)[/tex]

Divide both sides by [tex]\(-8.5\)[/tex]:
[tex]\[ z = \frac{78}{-8.5} \][/tex]

Step 6: Simplify the Result

Calculating the division gives us:
[tex]\[ z \approx -9.17647058823529 \][/tex]

Thus, the value of [tex]\(z\)[/tex] is:
[tex]\[ z \approx -9.176 \][/tex]

This completes the detailed, step-by-step solution to the given equation.

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