QuestionSolve for $x$ : $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $\frac{1}{3} x+\frac{1}{4} x-=x-7$ . We are solving for the variable $x$
3. The equation is a linear equation

STEP 2

First, we need to combine like terms on the left side of the equation. We can do this by adding $\frac{1}{} x$ and $\frac{1}{4} x$ together.
$\frac{1}{} x+\frac{1}{4} x-2 = \frac{7}{12} x -2$

STEP 3

Next, we need to isolate $x$ on one side of the equation. We can do this by subtracting $\frac{7}{12} x$ from both sides of the equation.
$-2 = x -7 - \frac{7}{12} x$

STEP 4

implify the right side of the equation by combining like terms.
$-2 = \frac{}{12} x -7$

STEP 5

Next, we need to isolate $x$ on one side of the equation. We can do this by adding7 to both sides of the equation.
$5 = \frac{5}{12} x$

STEP 6

Finally, we can solve for $x$ by multiplying both sides of the equation by $\frac{12}{5}$ .
$x = \frac{12}{5} \times5$

STEP 7

implify the right side of the equation to find the value of $x$ .
$x =12$ So, the solution to the equation $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ is $x =12$ .

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QuestionSolve for $x$ : $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ .

Studdy Solution

STEP 1

Assumptions1. The equation given is $\frac{1}{3} x+\frac{1}{4} x-=x-7$ . We are solving for the variable $x$
3. The equation is a linear equation

STEP 2

First, we need to combine like terms on the left side of the equation. We can do this by adding $\frac{1}{} x$ and $\frac{1}{4} x$ together.
$\frac{1}{} x+\frac{1}{4} x-2 = \frac{7}{12} x -2$

STEP 3

Next, we need to isolate $x$ on one side of the equation. We can do this by subtracting $\frac{7}{12} x$ from both sides of the equation.
$-2 = x -7 - \frac{7}{12} x$

STEP 4

implify the right side of the equation by combining like terms.
$-2 = \frac{}{12} x -7$

STEP 5

Next, we need to isolate $x$ on one side of the equation. We can do this by adding7 to both sides of the equation.
$5 = \frac{5}{12} x$

STEP 6

Finally, we can solve for $x$ by multiplying both sides of the equation by $\frac{12}{5}$ .
$x = \frac{12}{5} \times5$

STEP 7

implify the right side of the equation to find the value of $x$ .
$x =12$ So, the solution to the equation $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ is $x =12$ .

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QuestionSolve for xxx: 13x+14x−2=x−7\frac{1}{3} x+\frac{1}{4} x-2=x-731​x+41​x−2=x−7.

Studdy Solution

STEP 1

Assumptions1. The equation given is 13x+14x−=x−7\frac{1}{3} x+\frac{1}{4} x-=x-731​x+41​x−=x−7 . We are solving for the variable xxx3. The equation is a linear equation

STEP 2

First, we need to combine like terms on the left side of the equation. We can do this by adding 1x\frac{1}{} x1​x and 14x\frac{1}{4} x41​x together.1x+14x−2=712x−2\frac{1}{} x+\frac{1}{4} x-2 = \frac{7}{12} x -21​x+41​x−2=127​x−2

STEP 3

Next, we need to isolate xxx on one side of the equation. We can do this by subtracting 712x\frac{7}{12} x127​x from both sides of the equation.−2=x−7−712x-2 = x -7 - \frac{7}{12} x−2=x−7−127​x

STEP 4

implify the right side of the equation by combining like terms.−2=12x−7-2 = \frac{}{12} x -7−2=12​x−7

STEP 5

Next, we need to isolate xxx on one side of the equation. We can do this by adding7 to both sides of the equation.5=512x5 = \frac{5}{12} x5=125​x

STEP 6

Finally, we can solve for xxx by multiplying both sides of the equation by 125\frac{12}{5}512​.x=125×5x = \frac{12}{5} \times5x=512​×5

STEP 7

implify the right side of the equation to find the value of xxx.x=12x =12x=12So, the solution to the equation 13x+14x−2=x−7\frac{1}{3} x+\frac{1}{4} x-2=x-731​x+41​x−2=x−7 is x=12x =12x=12.

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QuestionSolve for $x$ : $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ .

Assumptions1. The equation given is $\frac{1}{3} x+\frac{1}{4} x-=x-7$ . We are solving for the variable $x$
3. The equation is a linear equation

First, we need to combine like terms on the left side of the equation. We can do this by adding $\frac{1}{} x$ and $\frac{1}{4} x$ together.
$\frac{1}{} x+\frac{1}{4} x-2 = \frac{7}{12} x -2$

Next, we need to isolate $x$ on one side of the equation. We can do this by subtracting $\frac{7}{12} x$ from both sides of the equation.
$-2 = x -7 - \frac{7}{12} x$

implify the right side of the equation by combining like terms.
$-2 = \frac{}{12} x -7$

Next, we need to isolate $x$ on one side of the equation. We can do this by adding7 to both sides of the equation.
$5 = \frac{5}{12} x$

Finally, we can solve for $x$ by multiplying both sides of the equation by $\frac{12}{5}$ .
$x = \frac{12}{5} \times5$

implify the right side of the equation to find the value of $x$ .
$x =12$ So, the solution to the equation $\frac{1}{3} x+\frac{1}{4} x-2=x-7$ is $x =12$ .