Questions: Solve the linear equation using equivalent equations to isolate the variable. Write your solution as an integer, as a simplified fraction, or as a decimal number 9x - 5x + 7/15 = 7/5

Solve the linear equation using equivalent equations to isolate the variable. Write your solution as an integer, as a simplified fraction, or as a decimal number 9x - 5x + 7/15 = 7/5
Transcript text: Solve the linear equation using equivalent equations to isolate the variable. Write your solution as an integer, as a simplified fraction, or as a decimal number \[ 9 x-5 x+\frac{7}{15}=\frac{7}{5} \]
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Solution

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Solution Steps

To solve the linear equation \( 9x - 5x + \frac{7}{15} = \frac{7}{5} \), we need to follow these steps:

  1. Combine like terms on the left-hand side.
  2. Isolate the variable \( x \) by moving the constant term to the right-hand side.
  3. Solve for \( x \) by performing the necessary arithmetic operations.
Step 1: Combine Like Terms

We start with the equation: \[ 9x - 5x + \frac{7}{15} = \frac{7}{5} \] Combining the terms involving \( x \) gives: \[ 4x + \frac{7}{15} = \frac{7}{5} \]

Step 2: Isolate the Variable

Next, we isolate \( x \) by moving \( \frac{7}{15} \) to the right side: \[ 4x = \frac{7}{5} - \frac{7}{15} \] To perform the subtraction, we need a common denominator. The least common multiple of 5 and 15 is 15: \[ \frac{7}{5} = \frac{21}{15} \] Thus, we have: \[ 4x = \frac{21}{15} - \frac{7}{15} = \frac{14}{15} \]

Step 3: Solve for \( x \)

Now, we divide both sides by 4 to solve for \( x \): \[ x = \frac{14}{15} \div 4 = \frac{14}{15} \cdot \frac{1}{4} = \frac{14}{60} = \frac{7}{30} \]

Final Answer

The solution to the equation is: \[ \boxed{x = \frac{7}{30}} \]

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