QuestionSolve the equation: $\frac{x}{5}-4=\frac{x}{4}-6$ .

Studdy Solution

STEP 1

Assumptions1. The equation we need to solve is $\frac{x}{5}-4=\frac{x}{4}-6$ . We are solving for the variable $x$
3. We are assuming that $x$ is a real number

STEP 2

First, we will isolate the terms with $x$ on one side of the equation and constants on the other side. We can do this by adding $4$ to both sides and subtracting $\frac{x}{4}$ from both sides.
$\frac{x}{5}-\frac{x}{4} = -6 +4$

STEP 3

implify the right side of the equation.
$\frac{x}{5}-\frac{x}{} = -2$

STEP 4

To make it easier to subtract the fractions, we will find a common denominator for $\frac{x}{}$ and $\frac{x}{4}$ . The least common multiple of $$ and $4$ is $20$, so we will multiply the numerator and denominator of each fraction by the necessary factor to get the denominator to be $20$.
$\frac{4x}{20}-\frac{x}{20} = -2$

STEP 5

Now, subtract the fractions on the left side of the equation.
$\frac{-x}{20} = -2$

STEP 6

To isolate $x$ , we will multiply both sides of the equation by $-20$ .
$x = -2 \times -20$

STEP 7

Calculate the value of $x$ .
$x =40$ So, the solution to the equation is $x =40$ .

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QuestionSolve the equation: $\frac{x}{5}-4=\frac{x}{4}-6$ .

Studdy Solution

STEP 1

Assumptions1. The equation we need to solve is $\frac{x}{5}-4=\frac{x}{4}-6$ . We are solving for the variable $x$
3. We are assuming that $x$ is a real number

STEP 2

First, we will isolate the terms with $x$ on one side of the equation and constants on the other side. We can do this by adding $4$ to both sides and subtracting $\frac{x}{4}$ from both sides.
$\frac{x}{5}-\frac{x}{4} = -6 +4$

STEP 3

implify the right side of the equation.
$\frac{x}{5}-\frac{x}{} = -2$

STEP 4

STEP 5

Now, subtract the fractions on the left side of the equation.
$\frac{-x}{20} = -2$

STEP 6

To isolate $x$ , we will multiply both sides of the equation by $-20$ .
$x = -2 \times -20$

STEP 7

Calculate the value of $x$ .
$x =40$ So, the solution to the equation is $x =40$ .

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QuestionSolve the equation: x5−4=x4−6\frac{x}{5}-4=\frac{x}{4}-65x​−4=4x​−6.

Studdy Solution

STEP 1

Assumptions1. The equation we need to solve is x5−4=x4−6\frac{x}{5}-4=\frac{x}{4}-65x​−4=4x​−6 . We are solving for the variable xxx3. We are assuming that xxx is a real number

STEP 2

First, we will isolate the terms with xxx on one side of the equation and constants on the other side. We can do this by adding 444 to both sides and subtracting x4\frac{x}{4}4x​ from both sides.x5−x4=−6+4\frac{x}{5}-\frac{x}{4} = -6 +45x​−4x​=−6+4

STEP 3

implify the right side of the equation.x5−x=−2\frac{x}{5}-\frac{x}{} = -25x​−x​=−2

STEP 4

STEP 5

Now, subtract the fractions on the left side of the equation.−x20=−2\frac{-x}{20} = -220−x​=−2

STEP 6

To isolate xxx, we will multiply both sides of the equation by −20-20−20.x=−2×−20x = -2 \times -20x=−2×−20

STEP 7

Calculate the value of xxx.x=40x =40x=40So, the solution to the equation is x=40x =40x=40.

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QuestionSolve the equation: $\frac{x}{5}-4=\frac{x}{4}-6$ .

Assumptions1. The equation we need to solve is $\frac{x}{5}-4=\frac{x}{4}-6$ . We are solving for the variable $x$
3. We are assuming that $x$ is a real number

First, we will isolate the terms with $x$ on one side of the equation and constants on the other side. We can do this by adding $4$ to both sides and subtracting $\frac{x}{4}$ from both sides.
$\frac{x}{5}-\frac{x}{4} = -6 +4$

implify the right side of the equation.
$\frac{x}{5}-\frac{x}{} = -2$

Now, subtract the fractions on the left side of the equation.
$\frac{-x}{20} = -2$

To isolate $x$ , we will multiply both sides of the equation by $-20$ .
$x = -2 \times -20$

Calculate the value of $x$ .
$x =40$ So, the solution to the equation is $x =40$ .