QuestionSolve for $v$ . $\frac{7}{4} v-\frac{8}{5}=-\frac{2}{3}$
Simplify your answer as much as possible. $v=$

Studdy Solution

STEP 1

1. The equation $\frac{7}{4} v - \frac{8}{5} = -\frac{2}{3}$ is a linear equation in one variable, $v$ .
2. We need to isolate $v$ on one side of the equation.
3. The solution involves basic algebraic operations, including addition, subtraction, and multiplication of fractions.

STEP 2

1. Eliminate the constant term from one side of the equation.
2. Isolate the variable $v$ by performing algebraic operations.
3. Simplify the solution.

STEP 3

First, eliminate the constant term $-\frac{8}{5}$ from the left side by adding $\frac{8}{5}$ to both sides of the equation:
$\frac{7}{4} v - \frac{8}{5} + \frac{8}{5} = -\frac{2}{3} + \frac{8}{5}$
Simplify:
$\frac{7}{4} v = -\frac{2}{3} + \frac{8}{5}$

STEP 4

To add the fractions on the right side, find a common denominator. The least common multiple of 3 and 5 is 15.
Convert each fraction:
$-\frac{2}{3} = -\frac{10}{15}, \quad \frac{8}{5} = \frac{24}{15}$
Add the fractions:
$-\frac{10}{15} + \frac{24}{15} = \frac{14}{15}$
So the equation becomes:
$\frac{7}{4} v = \frac{14}{15}$

STEP 5

To isolate $v$ , multiply both sides by the reciprocal of $\frac{7}{4}$ , which is $\frac{4}{7}$ :
$v = \frac{14}{15} \times \frac{4}{7}$

STEP 6

Multiply the fractions:
$v = \frac{14 \times 4}{15 \times 7} = \frac{56}{105}$

STEP 7

Simplify $\frac{56}{105}$ by finding the greatest common divisor (GCD) of 56 and 105, which is 7.
Divide both the numerator and the denominator by 7:
$v = \frac{56 \div 7}{105 \div 7} = \frac{8}{15}$
The simplified solution is:
$v = \frac{8}{15}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms