Solving 2-Step Equations

Review how to solve 2-step equations using rules of equality.

Solve the following 2 equations.

1. \(8(4x - 7.5) = 84\)

2. \(-7 = \frac{{y - 9}}{8}\)

1. \(8(4x - 7.5) = 84\)

First, we'll distribute \(8\) to \(4x - 7.5\):

\[8 \cdot 4x - 8 \cdot 7.5 = 84\]

This simplifies to:

\[32x - 60 = 84\]

Next, let's isolate the variable \(x\) by adding \(60\) to both sides:

\[32x - 60 + 60 = 84 + 60\]

Which simplifies to:

\[32x = 144\]

Now, divide both sides by \(32\) to solve for \(x\):

\[\frac{32x}{32} = \frac{144}{32}\]

This simplifies to:

\[x = \frac{144}{32} = 4.5\]

So, the solution to the equation \(8(4x - 7.5) = 84\) is \(x = 4.5\).

2. \(-7 = \frac{y - 9}{8}\)

To solve for \(y\), we'll first isolate the fraction term by multiplying both sides by \(8\):

\[8 \cdot (-7) = 8 \cdot \frac{y - 9}{8}\]

This simplifies to:

\[-56 = y - 9\]

Next, we'll isolate \(y\) by adding \(9\) to both sides:

\[-56 + 9 = y - 9 + 9\]

Which simplifies to:

\[-47 = y\]

So, the solution to the equation \(-7 = \frac{y - 9}{8}\) is \(y = -47\).

Let me know if you need further clarification on any step!

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