Solve for X in the Equation: 6/10 - 30x + 1/4 = 6/8 - 16x

Video Solution

Solution Steps

00:12 Let's start by finding X.

00:15 First, rearrange the equation so X is on one side by itself.

00:46 Now, break down 6 into two times three, and 10 into two times five.

00:56 Great job! Next, simplify any terms you can.

01:05 Let's again factor 6 into two and three, and 8 into two and four.

01:11 Keep it up! Simplify any possible terms here too.

01:20 Gather all similar terms together.

01:36 Then multiply by the denominators to get a common denominator.

02:03 Now, isolate X on one side of the equation.

02:11 Remember, multiply numerators together and denominators together.

02:16 And that's how you find the solution to this problem.

Step-by-Step Solution

To solve the equation $\frac{6}{10} - 30x + \frac{1}{4} = \frac{6}{8} - 16x$ , follow these steps:

Step 1: Simplify the fractions involved. We have $\frac{6}{10} = \frac{3}{5}$ and $\frac{6}{8} = \frac{3}{4}$ .
Step 2: The equation becomes $\frac{3}{5} - 30x + \frac{1}{4} = \frac{3}{4} - 16x$ .
Step 3: Combine the constant terms on each side. The left side is $\frac{3}{5} + \frac{1}{4}$ . Find a common denominator, which is 20:

\frac{3}{5} = \frac{12}{20}

\frac{1}{4} = \frac{5}{20}

So,

\frac{3}{5} + \frac{1}{4} = \frac{12}{20} + \frac{5}{20} = \frac{17}{20}

Step 4: Substitute back into the equation: $\frac{17}{20} - 30x = \frac{3}{4} - 16x$ .
Step 5: Simplify the right side. $\frac{3}{4} = \frac{15}{20}$ , so the equation becomes $\frac{17}{20} - 30x = \frac{15}{20} - 16x$ .
Step 6: Subtract $\frac{15}{20}$ from both sides to get $\frac{17}{20} - \frac{15}{20} - 30x = -16x$ :

\frac{17}{20} - \frac{15}{20} = \frac{2}{20} = \frac{1}{10}

So, the equation becomes

\frac{1}{10} - 30x = -16x

Step 7: Rearrange the equation to solve for $x$ by adding $30x$ to both sides: $\frac{1}{10} = 30x - 16x$ .
Step 8: Simplify the equation: $\frac{1}{10} = 14x$ .
Step 9: Divide both sides by 14 to solve for $x$ : $x = \frac{1}{10 \times 14} = \frac{1}{140}$ .

Therefore, the solution to the problem is $x = \frac{1}{140}$ .