Respuesta :

Answer:

Y equals -1/5

Space

Answer:

y = -0.2

General Formulas and Concepts:

Pre-Algebra

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

Step 1: Define equation

[tex]\frac{3.6}{0.2(6y + 1)} =\frac{9}{0.5y}[/tex]

Step 2: Solve for y

  1. Distribute 0.2:                              [tex]\frac{3.6}{1.2y + 0.2} =\frac{9}{0.5y}[/tex]
  2. Cross-multiply:                             [tex]9(1.2y + 0.2) =3.6(0.5y)}[/tex]
  3. Distribute:                                    [tex]10.8y + 1.8 =1.8y[/tex]
  4. Subtract 1.8y on both sides:       [tex]9y + 1.8 =0[/tex]
  5. Subtract 1.8 on both sides:         [tex]9y = -1.8[/tex]
  6. Divide both sides by 9:               [tex]y = -0.2[/tex]

Step 3: Check

Plug in y to verify it's a solution.

  1. Substitute:                    [tex]\frac{3.6}{0.2(6(-0.2) + 1)} =\frac{9}{0.5(-0.2)}[/tex]
  2. Multiply:                        [tex]\frac{3.6}{0.2(-1.2 + 1)} =\frac{9}{-0.1}[/tex]
  3. Add:                              [tex]\frac{3.6}{0.2(-0.2)} =\frac{9}{-0.1}[/tex]
  4. Multiply:                        [tex]\frac{3.6}{-0.04} =\frac{9}{-0.1}[/tex]
  5. Divide:                          [tex]-90=-90[/tex]

Here we see that -90 does indeed equal -90. ∴ y = -0.2 is indeed a solution of the equation.

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