Math / Algebra

Question $\frac{1}{2} v-12+20=14$

Studdy Solution

STEP 1

1. The equation $\frac{1}{2} v - 12 + 20 = 14$ is a linear equation in one variable, $v$ .
2. The goal is to solve for $v$ .
3. Basic algebraic operations such as addition, subtraction, and multiplication will be used.

STEP 2

1. Simplify the equation.
2. Isolate the variable $v$ .
3. Check the solution by substituting it back into the original equation.

STEP 3

First, simplify the equation by combining like terms on the left-hand side. Combine $-12$ and $+20$ :
$\frac{1}{2} v + 8 = 14$

STEP 4

Next, isolate the term with the variable $v$ by subtracting 8 from both sides of the equation:
$\frac{1}{2} v + 8 - 8 = 14 - 8$
Simplify:
$\frac{1}{2} v = 6$

STEP 5

To solve for $v$ , multiply both sides of the equation by 2 to cancel out the fraction:
$2 \times \frac{1}{2} v = 2 \times 6$
Simplify:
$v = 12$

STEP 6

Check the solution by substituting $v = 12$ back into the original equation:
$\frac{1}{2} (12) - 12 + 20 = 14$
Simplify the left-hand side:
$6 - 12 + 20 = 14$
Combine the terms:
$14 = 14$
Both sides are equal, confirming that the solution is correct.
The solution is:
$\boxed{12}$

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Question $\frac{1}{2} v-12+20=14$

Studdy Solution

STEP 1

1. The equation $\frac{1}{2} v - 12 + 20 = 14$ is a linear equation in one variable, $v$ .
2. The goal is to solve for $v$ .
3. Basic algebraic operations such as addition, subtraction, and multiplication will be used.

STEP 2

1. Simplify the equation.
2. Isolate the variable $v$ .
3. Check the solution by substituting it back into the original equation.

STEP 3

First, simplify the equation by combining like terms on the left-hand side. Combine $-12$ and $+20$ :
$\frac{1}{2} v + 8 = 14$

STEP 4

Next, isolate the term with the variable $v$ by subtracting 8 from both sides of the equation:
$\frac{1}{2} v + 8 - 8 = 14 - 8$
Simplify:
$\frac{1}{2} v = 6$

STEP 5

To solve for $v$ , multiply both sides of the equation by 2 to cancel out the fraction:
$2 \times \frac{1}{2} v = 2 \times 6$
Simplify:
$v = 12$

STEP 6

Check the solution by substituting $v = 12$ back into the original equation:
$\frac{1}{2} (12) - 12 + 20 = 14$
Simplify the left-hand side:
$6 - 12 + 20 = 14$
Combine the terms:
$14 = 14$
Both sides are equal, confirming that the solution is correct.
The solution is:
$\boxed{12}$

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Question12v−12+20=14\frac{1}{2} v-12+20=1421​v−12+20=14

Studdy Solution

STEP 1

1. The equation 12v−12+20=14\frac{1}{2} v - 12 + 20 = 1421​v−12+20=14 is a linear equation in one variable, vvv.2. The goal is to solve for vvv.3. Basic algebraic operations such as addition, subtraction, and multiplication will be used.

STEP 2

1. Simplify the equation.2. Isolate the variable vvv.3. Check the solution by substituting it back into the original equation.

STEP 3

First, simplify the equation by combining like terms on the left-hand side. Combine −12-12−12 and +20+20+20:12v+8=14\frac{1}{2} v + 8 = 1421​v+8=14

STEP 4

Next, isolate the term with the variable vvv by subtracting 8 from both sides of the equation:12v+8−8=14−8\frac{1}{2} v + 8 - 8 = 14 - 821​v+8−8=14−8Simplify:12v=6\frac{1}{2} v = 621​v=6

STEP 5

To solve for vvv, multiply both sides of the equation by 2 to cancel out the fraction:2×12v=2×62 \times \frac{1}{2} v = 2 \times 62×21​v=2×6Simplify:v=12v = 12v=12

STEP 6

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Question $\frac{1}{2} v-12+20=14$

1. The equation $\frac{1}{2} v - 12 + 20 = 14$ is a linear equation in one variable, $v$ .
2. The goal is to solve for $v$ .
3. Basic algebraic operations such as addition, subtraction, and multiplication will be used.

1. Simplify the equation.
2. Isolate the variable $v$ .
3. Check the solution by substituting it back into the original equation.

First, simplify the equation by combining like terms on the left-hand side. Combine $-12$ and $+20$ :
$\frac{1}{2} v + 8 = 14$

Next, isolate the term with the variable $v$ by subtracting 8 from both sides of the equation:
$\frac{1}{2} v + 8 - 8 = 14 - 8$
Simplify:
$\frac{1}{2} v = 6$

To solve for $v$ , multiply both sides of the equation by 2 to cancel out the fraction:
$2 \times \frac{1}{2} v = 2 \times 6$
Simplify:
$v = 12$