Solved on Jan 18, 2024

Solve for the value of $v$ given the equation $v-\frac{3}{8}=-\frac{3}{4}$ .

STEP 1

Assumptions
1. We are given the equation $v - \frac{3}{8} = -\frac{3}{4}$ .
2. We need to solve for the variable $v$ .

STEP 2

To isolate the variable $v$ , we need to add $\frac{3}{8}$ to both sides of the equation to cancel out the $-\frac{3}{8}$ on the left side.
$v - \frac{3}{8} + \frac{3}{8} = -\frac{3}{4} + \frac{3}{8}$

STEP 3

Simplify the left side of the equation by combining like terms.
$v = -\frac{3}{4} + \frac{3}{8}$

STEP 4

To combine the fractions on the right side, we need a common denominator. The least common denominator (LCD) for 4 and 8 is 8.

STEP 5

Convert $-\frac{3}{4}$ to have the denominator of 8.
$-\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8}$

STEP 6

Now that both fractions have the same denominator, we can add them together.
$v = -\frac{6}{8} + \frac{3}{8}$

STEP 7

Add the numerators and keep the common denominator.
$v = \frac{-6 + 3}{8}$

STEP 8

Simplify the numerator.
$v = \frac{-3}{8}$
So the solution for $v$ is $-\frac{3}{8}$ .

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Solve for the value of $v$ given the equation $v-\frac{3}{8}=-\frac{3}{4}$ .

STEP 1

Assumptions
1. We are given the equation $v - \frac{3}{8} = -\frac{3}{4}$ .
2. We need to solve for the variable $v$ .

STEP 2

To isolate the variable $v$ , we need to add $\frac{3}{8}$ to both sides of the equation to cancel out the $-\frac{3}{8}$ on the left side.
$v - \frac{3}{8} + \frac{3}{8} = -\frac{3}{4} + \frac{3}{8}$

STEP 3

Simplify the left side of the equation by combining like terms.
$v = -\frac{3}{4} + \frac{3}{8}$

STEP 4

To combine the fractions on the right side, we need a common denominator. The least common denominator (LCD) for 4 and 8 is 8.

STEP 5

Convert $-\frac{3}{4}$ to have the denominator of 8.
$-\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8}$

STEP 6

Now that both fractions have the same denominator, we can add them together.
$v = -\frac{6}{8} + \frac{3}{8}$

STEP 7

Add the numerators and keep the common denominator.
$v = \frac{-6 + 3}{8}$

STEP 8

Simplify the numerator.
$v = \frac{-3}{8}$
So the solution for $v$ is $-\frac{3}{8}$ .

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Solve for the value of vvv given the equation v−38=−34v-\frac{3}{8}=-\frac{3}{4}v−83​=−43​.

STEP 1

Assumptions1. We are given the equation v−38=−34v - \frac{3}{8} = -\frac{3}{4}v−83​=−43​.2. We need to solve for the variable vvv.

STEP 2

To isolate the variable vvv, we need to add 38\frac{3}{8}83​ to both sides of the equation to cancel out the −38-\frac{3}{8}−83​ on the left side.v−38+38=−34+38v - \frac{3}{8} + \frac{3}{8} = -\frac{3}{4} + \frac{3}{8}v−83​+83​=−43​+83​

STEP 3

Simplify the left side of the equation by combining like terms.v=−34+38v = -\frac{3}{4} + \frac{3}{8}v=−43​+83​

STEP 4

To combine the fractions on the right side, we need a common denominator. The least common denominator (LCD) for 4 and 8 is 8.

STEP 5

Convert −34-\frac{3}{4}−43​ to have the denominator of 8.−34=−3×24×2=−68-\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8}−43​=−4×23×2​=−86​

STEP 6

Now that both fractions have the same denominator, we can add them together.v=−68+38v = -\frac{6}{8} + \frac{3}{8}v=−86​+83​

STEP 7

Add the numerators and keep the common denominator.v=−6+38v = \frac{-6 + 3}{8}v=8−6+3​

STEP 8

Simplify the numerator.v=−38v = \frac{-3}{8}v=8−3​So the solution for vvv is −38-\frac{3}{8}−83​.

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Solve for the value of $v$ given the equation $v-\frac{3}{8}=-\frac{3}{4}$ .

Assumptions
1. We are given the equation $v - \frac{3}{8} = -\frac{3}{4}$ .
2. We need to solve for the variable $v$ .

To isolate the variable $v$ , we need to add $\frac{3}{8}$ to both sides of the equation to cancel out the $-\frac{3}{8}$ on the left side.
$v - \frac{3}{8} + \frac{3}{8} = -\frac{3}{4} + \frac{3}{8}$

Simplify the left side of the equation by combining like terms.
$v = -\frac{3}{4} + \frac{3}{8}$

Convert $-\frac{3}{4}$ to have the denominator of 8.
$-\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8}$

Now that both fractions have the same denominator, we can add them together.
$v = -\frac{6}{8} + \frac{3}{8}$

Add the numerators and keep the common denominator.
$v = \frac{-6 + 3}{8}$

Simplify the numerator.
$v = \frac{-3}{8}$
So the solution for $v$ is $-\frac{3}{8}$ .