Math / Algebra

Question(12) $\frac{1}{5} x+3=-\frac{1}{4} x+3$

Studdy Solution

STEP 1

1. The equation $\frac{1}{5}x + 3 = -\frac{1}{4}x + 3$ is a linear equation in one variable.
2. The goal is to solve for $x$ .
3. The equation involves fractions, which require careful manipulation.

STEP 2

1. Simplify the equation by eliminating the constant terms on both sides.
2. Combine like terms to isolate the variable $x$ .
3. Solve for $x$ .

STEP 3

First, observe that both sides of the equation have a constant term $+3$ . We can subtract $3$ from both sides to simplify the equation:
$\frac{1}{5}x + 3 - 3 = -\frac{1}{4}x + 3 - 3$
This simplifies to:
$\frac{1}{5}x = -\frac{1}{4}x$

STEP 4

Next, we need to combine the $x$ -terms. To do this, add $\frac{1}{4}x$ to both sides to get all $x$ -terms on one side:
$\frac{1}{5}x + \frac{1}{4}x = 0$

STEP 5

To combine the fractions, find a common denominator. The common denominator of 5 and 4 is 20. Convert each fraction:
$\frac{4}{20}x + \frac{5}{20}x = 0$
Combine the fractions:
$\frac{9}{20}x = 0$

STEP 6

To solve for $x$ , multiply both sides by the reciprocal of $\frac{9}{20}$ , which is $\frac{20}{9}$ :
$x = 0 \times \frac{20}{9}$
Simplify:
$x = 0$
The solution is:
$\boxed{0}$

Was this helpful?

Question(12) $\frac{1}{5} x+3=-\frac{1}{4} x+3$

Studdy Solution

STEP 1

1. The equation $\frac{1}{5}x + 3 = -\frac{1}{4}x + 3$ is a linear equation in one variable.
2. The goal is to solve for $x$ .
3. The equation involves fractions, which require careful manipulation.

STEP 2

1. Simplify the equation by eliminating the constant terms on both sides.
2. Combine like terms to isolate the variable $x$ .
3. Solve for $x$ .

STEP 3

First, observe that both sides of the equation have a constant term $+3$ . We can subtract $3$ from both sides to simplify the equation:
$\frac{1}{5}x + 3 - 3 = -\frac{1}{4}x + 3 - 3$
This simplifies to:
$\frac{1}{5}x = -\frac{1}{4}x$

STEP 4

Next, we need to combine the $x$ -terms. To do this, add $\frac{1}{4}x$ to both sides to get all $x$ -terms on one side:
$\frac{1}{5}x + \frac{1}{4}x = 0$

STEP 5

To combine the fractions, find a common denominator. The common denominator of 5 and 4 is 20. Convert each fraction:
$\frac{4}{20}x + \frac{5}{20}x = 0$
Combine the fractions:
$\frac{9}{20}x = 0$

STEP 6

To solve for $x$ , multiply both sides by the reciprocal of $\frac{9}{20}$ , which is $\frac{20}{9}$ :
$x = 0 \times \frac{20}{9}$
Simplify:
$x = 0$
The solution is:
$\boxed{0}$

Get Studdy

Studdy solves anything!

Start learning now

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

Question(12) 15x+3=−14x+3\frac{1}{5} x+3=-\frac{1}{4} x+351​x+3=−41​x+3

Studdy Solution

STEP 1

1. The equation 15x+3=−14x+3\frac{1}{5}x + 3 = -\frac{1}{4}x + 351​x+3=−41​x+3 is a linear equation in one variable.2. The goal is to solve for x x x.3. The equation involves fractions, which require careful manipulation.

STEP 2

1. Simplify the equation by eliminating the constant terms on both sides.2. Combine like terms to isolate the variable x x x.3. Solve for x x x.

STEP 3

STEP 4

Next, we need to combine the x x x-terms. To do this, add 14x\frac{1}{4}x41​x to both sides to get all x x x-terms on one side:15x+14x=0 \frac{1}{5}x + \frac{1}{4}x = 0 51​x+41​x=0

STEP 5

To combine the fractions, find a common denominator. The common denominator of 5 and 4 is 20. Convert each fraction:420x+520x=0 \frac{4}{20}x + \frac{5}{20}x = 0 204​x+205​x=0Combine the fractions:920x=0 \frac{9}{20}x = 0 209​x=0

STEP 6

To solve for x x x, multiply both sides by the reciprocal of 920\frac{9}{20}209​, which is 209\frac{20}{9}920​:x=0×209 x = 0 \times \frac{20}{9} x=0×920​Simplify:x=0 x = 0 x=0 The solution is:0 \boxed{0} 0​

Get Studdy

Studdy solves anything!

Start learning now

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

Question(12) $\frac{1}{5} x+3=-\frac{1}{4} x+3$

1. The equation $\frac{1}{5}x + 3 = -\frac{1}{4}x + 3$ is a linear equation in one variable.
2. The goal is to solve for $x$ .
3. The equation involves fractions, which require careful manipulation.

1. Simplify the equation by eliminating the constant terms on both sides.
2. Combine like terms to isolate the variable $x$ .
3. Solve for $x$ .

Next, we need to combine the $x$ -terms. To do this, add $\frac{1}{4}x$ to both sides to get all $x$ -terms on one side:
$\frac{1}{5}x + \frac{1}{4}x = 0$

To combine the fractions, find a common denominator. The common denominator of 5 and 4 is 20. Convert each fraction:
$\frac{4}{20}x + \frac{5}{20}x = 0$
Combine the fractions:
$\frac{9}{20}x = 0$

To solve for $x$ , multiply both sides by the reciprocal of $\frac{9}{20}$ , which is $\frac{20}{9}$ :
$x = 0 \times \frac{20}{9}$
Simplify:
$x = 0$
The solution is:
$\boxed{0}$