Solved on Nov 08, 2023

Solve the equation $\frac{1}{2}(x-9)+\frac{1}{3}(x+5)=-2$ for $x$ .

STEP 1

Assumptions1. The given equation is $\frac{1}{}(x-9)+\frac{1}{3}(x+5)=-$ . . We are required to find the value of $x$ .

STEP 2

First, we will distribute the fractions to the terms inside the parentheses. This can be done by multiplying each term inside the parentheses by the fraction outside.
$\frac{1}{2}x - \frac{9}{2} + \frac{1}{}x + \frac{5}{} = -2$

STEP 3

Next, we will combine like terms on the left side of the equation. Like terms are terms that have the same variable and exponent. In this case, the like terms are $\frac{1}{2}x$ and $\frac{1}{3}x$ , and $-\frac{9}{2}$ and $\frac{5}{3}$ .
$\left(\frac{1}{2}x + \frac{1}{3}x\right) + \left(-\frac{9}{2} + \frac{5}{3}\right) = -2$

STEP 4

To add the fractions $\frac{1}{2}x$ and $\frac{1}{3}x$ , we need to find a common denominator. The least common denominator (LCD) of2 and3 is6. Multiply each term by the factor needed to get the LCD.
$\left(\frac{3}{6}x + \frac{2}{6}x\right) + \left(-\frac{9}{2} + \frac{}{3}\right) = -2$

STEP 5

Now, add the fractions with the common denominator.
$\frac{5}{}x + \left(-\frac{9}{2} + \frac{5}{3}\right) = -2$

STEP 6

Similarly, to add the fractions $-\frac{9}{2}$ and $\frac{5}{3}$ , we need to find a common denominator. The least common denominator (LCD) of2 and3 is6. Multiply each term by the factor needed to get the LCD.
$\frac{5}{6}x + \left(-\frac{27}{6} + \frac{10}{6}\right) = -2$

STEP 7

Now, add the fractions with the common denominator.
$\frac{5}{6}x - \frac{17}{6} = -2$

STEP 8

Next, we will isolate the term with $x$ on one side of the equation. We can do this by adding $\frac{17}{6}$ to both sides of the equation.
$\frac{5}{6}x = -2 + \frac{17}{6}$

STEP 9

implify the right side of the equation.
$\frac{5}{6}x = -\frac{12}{6} + \frac{17}{6}$

STEP 10

Add the fractions on the right side.
$\frac{5}{6}x = \frac{5}{6}$

STEP 11

Finally, to solve for $x$ , we will divide both sides of the equation by $\frac{5}{6}$ .
$x = \frac{\frac{5}{6}}{\frac{5}{6}}$

STEP 12

implify the right side of the equation.
$x =$ So, the solution to the equation is $x =$ .

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Solve the equation $\frac{1}{2}(x-9)+\frac{1}{3}(x+5)=-2$ for $x$ .

STEP 1

Assumptions1. The given equation is $\frac{1}{}(x-9)+\frac{1}{3}(x+5)=-$ . . We are required to find the value of $x$ .

STEP 2

First, we will distribute the fractions to the terms inside the parentheses. This can be done by multiplying each term inside the parentheses by the fraction outside.
$\frac{1}{2}x - \frac{9}{2} + \frac{1}{}x + \frac{5}{} = -2$

STEP 3

STEP 4

To add the fractions $\frac{1}{2}x$ and $\frac{1}{3}x$ , we need to find a common denominator. The least common denominator (LCD) of2 and3 is6. Multiply each term by the factor needed to get the LCD.
$\left(\frac{3}{6}x + \frac{2}{6}x\right) + \left(-\frac{9}{2} + \frac{}{3}\right) = -2$

STEP 5

Now, add the fractions with the common denominator.
$\frac{5}{}x + \left(-\frac{9}{2} + \frac{5}{3}\right) = -2$

STEP 6

Similarly, to add the fractions $-\frac{9}{2}$ and $\frac{5}{3}$ , we need to find a common denominator. The least common denominator (LCD) of2 and3 is6. Multiply each term by the factor needed to get the LCD.
$\frac{5}{6}x + \left(-\frac{27}{6} + \frac{10}{6}\right) = -2$

STEP 7

Now, add the fractions with the common denominator.
$\frac{5}{6}x - \frac{17}{6} = -2$

STEP 8

Next, we will isolate the term with $x$ on one side of the equation. We can do this by adding $\frac{17}{6}$ to both sides of the equation.
$\frac{5}{6}x = -2 + \frac{17}{6}$

STEP 9

implify the right side of the equation.
$\frac{5}{6}x = -\frac{12}{6} + \frac{17}{6}$

STEP 10

Add the fractions on the right side.
$\frac{5}{6}x = \frac{5}{6}$

STEP 11

Finally, to solve for $x$ , we will divide both sides of the equation by $\frac{5}{6}$ .
$x = \frac{\frac{5}{6}}{\frac{5}{6}}$

STEP 12

implify the right side of the equation.
$x =$ So, the solution to the equation is $x =$ .

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Solve the equation 12(x−9)+13(x+5)=−2\frac{1}{2}(x-9)+\frac{1}{3}(x+5)=-221​(x−9)+31​(x+5)=−2 for xxx.

STEP 1

Assumptions1. The given equation is 1(x−9)+13(x+5)=−\frac{1}{}(x-9)+\frac{1}{3}(x+5)=-1​(x−9)+31​(x+5)=−. . We are required to find the value of xxx.

STEP 2

First, we will distribute the fractions to the terms inside the parentheses. This can be done by multiplying each term inside the parentheses by the fraction outside.12x−92+1x+5=−2\frac{1}{2}x - \frac{9}{2} + \frac{1}{}x + \frac{5}{} = -221​x−29​+1​x+5​=−2

STEP 3

STEP 4

STEP 5

Now, add the fractions with the common denominator.5x+(−92+53)=−2\frac{5}{}x + \left(-\frac{9}{2} + \frac{5}{3}\right) = -25​x+(−29​+35​)=−2

STEP 6

STEP 7

Now, add the fractions with the common denominator.56x−176=−2\frac{5}{6}x - \frac{17}{6} = -265​x−617​=−2

STEP 8

Next, we will isolate the term with xxx on one side of the equation. We can do this by adding 176\frac{17}{6}617​ to both sides of the equation.56x=−2+176\frac{5}{6}x = -2 + \frac{17}{6}65​x=−2+617​

STEP 9

implify the right side of the equation.56x=−126+176\frac{5}{6}x = -\frac{12}{6} + \frac{17}{6}65​x=−612​+617​

STEP 10

Add the fractions on the right side.56x=56\frac{5}{6}x = \frac{5}{6}65​x=65​

STEP 11

Finally, to solve for xxx, we will divide both sides of the equation by 56\frac{5}{6}65​.x=5656x = \frac{\frac{5}{6}}{\frac{5}{6}}x=65​65​​

STEP 12

implify the right side of the equation.x=x =x=So, the solution to the equation is x=x =x=.

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

Solve the equation $\frac{1}{2}(x-9)+\frac{1}{3}(x+5)=-2$ for $x$ .

Assumptions1. The given equation is $\frac{1}{}(x-9)+\frac{1}{3}(x+5)=-$ . . We are required to find the value of $x$ .

First, we will distribute the fractions to the terms inside the parentheses. This can be done by multiplying each term inside the parentheses by the fraction outside.
$\frac{1}{2}x - \frac{9}{2} + \frac{1}{}x + \frac{5}{} = -2$

Now, add the fractions with the common denominator.
$\frac{5}{}x + \left(-\frac{9}{2} + \frac{5}{3}\right) = -2$

Now, add the fractions with the common denominator.
$\frac{5}{6}x - \frac{17}{6} = -2$

Next, we will isolate the term with $x$ on one side of the equation. We can do this by adding $\frac{17}{6}$ to both sides of the equation.
$\frac{5}{6}x = -2 + \frac{17}{6}$

implify the right side of the equation.
$\frac{5}{6}x = -\frac{12}{6} + \frac{17}{6}$

Add the fractions on the right side.
$\frac{5}{6}x = \frac{5}{6}$

Finally, to solve for $x$ , we will divide both sides of the equation by $\frac{5}{6}$ .
$x = \frac{\frac{5}{6}}{\frac{5}{6}}$

implify the right side of the equation.
$x =$ So, the solution to the equation is $x =$ .