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 \[ 9 x-5 x+\frac{7}{15}=\frac{7}{5} \]
failed

Solution

failed
failed

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: \[ \boxed{x = \frac{7}{30}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A same-size iron ball and wooden ball are dropped simultaneously from a tower and reach the ground at the same time. The iron ball has a greater a. all of the above b. acceleration. c. none of the above d. momentum. e. speed.
failedAnswered
Determine whether this table represents a probability distribution. x P(x) ------ 0 0.3 1 0.1 2 0.25 3 0.3 Yes, it is a probability distribution No, it is not a probability distribution
failedAnswered
The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "hole Use the graph to complete the following. (a) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -4 4 -3 0 None y-intercept(s): 0 -3 -4 None (b) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): x=-3 Horizontal asymptote(s): y=0 (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range:
failedAnswered
Use the fact that the mean of a geometric distribution is μ=1/p and the variance is σ^2=q/p^2. A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 1/100. Let x be the number of times you play the lottery before winning the first time. (a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs 1 to play and winners are paid 900. Would you expect to make or lose money playing this lottery? Explain. (a) The mean is (Type an integer or a decimal.)
failedAnswered
If the interest rate is 10 percent and cash flows are 1,000 at the end of year one and 2,000 at the end of year two, then the present value of these cash flows is Multiple Choice 2,562. 3,200. 439. 3,000.