OpenStudy (anonymous):

Solve for x see pic

6 years ago
OpenStudy (anonymous):
6 years ago

OpenStudy (mathstudent55):

First, distribute the -3 on the right side. Then multiply both sides by the LCD to get rid of fractions. Then collect like terms.

6 years ago
OpenStudy (anonymous):

frst take all x terms on one side then constant terms on left

6 years ago
OpenStudy (anonymous):

LCD is 4??

6 years ago
OpenStudy (mathstudent55):

The LCD is the smallest number that 2, 3, and 4 divide _into_ evenly, so it can't possibly be smaller than 4.

6 years ago
OpenStudy (anonymous):

(1)/(3)*x+(1)/(2)=-3((3)/(4)*x-1) Multiply (1)/(3) by x to get (x)/(3). (x)/(3)+(1)/(2)=-3((3)/(4)*x-1) Multiply (3)/(4) by x to get (3x)/(4). (x)/(3)+(1)/(2)=-3((3x)/(4)-1) Multiply -3 by each term inside the parentheses. (x)/(3)+(1)/(2)=-(9x)/(4)+3 Since (1)/(2) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (1)/(2) from both sides. (x)/(3)=-(1)/(2)-(9x)/(4)+3 Simplify the right-hand side of the equation. (x)/(3)=-(9x)/(4)+(5)/(2) Find the LCD (least common denominator) of (x)/(3)-(9x)/(4)+(5)/(2). Least common denominator: 12 Multiply each term in the equation by 12 in order to remove all the denominators from the equation. (x)/(3)*12=-(9x)/(4)*12+(5)/(2)*12 Simplify the left-hand side of the equation by canceling the common factors. 4x=-(9x)/(4)*12+(5)/(2)*12 Simplify the right-hand side of the equation by simplifying each term. 4x=-27x+30 Since -27x contains the variable to solve for, move it to the left-hand side of the equation by adding 27x to both sides. 4x+27x=30 Since 4x and 27x are like terms, add 27x to 4x to get 31x. 31x=30 Divide each term in the equation by 31. (31x)/(31)=(30)/(31) Simplify the left-hand side of the equation by canceling the common factors. x=30/31

6 years ago
OpenStudy (mathstudent55):

LCD (= least common denominator) is also called the LCM (= least common multiple). What number is the smallest multiple of 2, 3, and 4? Here are the first several multiples of 2, 3, and 4. Pick the smallest common one: 2: 2, 4, 6, 8, 10, 12, 14, 16, 18 3: 3, 9, 12, 15, 18, 21 4: 4, 8, 12, 16, 20, 24

6 years ago
OpenStudy (anonymous):

Multiply each side by 12.\[12\left(\frac{1}{3}x+\frac{1}{2}\right)=\left(-3\left(\frac{3}{4}x-1\right)\right)12 \]\[4 x+6=36-27 x \]

6 years ago
OpenStudy (mathstudent55):

|dw:1359440015052:dw|

6 years ago