Questions: 0.5=6(q-5)-19

0.5=6(q-5)-19
Transcript text: $0.5=6(q-5)-19$
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Solution

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Solution Steps

To solve the equation \(0.5 = 6(q - 5) - 19\), we need to isolate the variable \(q\). Here are the high-level steps:

  1. Simplify the equation by distributing the 6.
  2. Combine like terms.
  3. Isolate \(q\) by performing algebraic operations.
Step 1: Distribute the 6

First, we distribute the 6 in the equation \(0.5 = 6(q - 5) - 19\): \[ 0.5 = 6q - 30 - 19 \]

Step 2: Combine Like Terms

Next, we combine the constants on the right-hand side: \[ 0.5 = 6q - 49 \]

Step 3: Isolate \(q\)

To isolate \(q\), we add 49 to both sides of the equation: \[ 0.5 + 49 = 6q \] \[ 49.5 = 6q \]

Step 4: Solve for \(q\)

Finally, we divide both sides by 6 to solve for \(q\): \[ q = \frac{49.5}{6} \] \[ q = 8.25 \]

Final Answer

\[ q = \frac{99}{12} = \frac{33}{4} \] \[ \boxed{q = \frac{33}{4}} \]

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