Question

solve the equation: 2/7+1/3x-1/4=2/3x

Answer 1

(2)/(7)+(1)/(3)*x-(1)/(4)=(2)/(3)*x

Multiply 1 by x to get x.
(2)/(7)+(x)/(3)-(1)/(4)=(2)/(3)*x

Reorder the polynomial (2)/(7)+(x)/(3)-(1)/(4) alphabetically from left to right, starting with the highest order term.
(x)/(3)+(2)/(7)-(1)/(4)=(2)/(3)*x

Multiply 2 by x to get 2x.
(x)/(3)+(2)/(7)-(1)/(4)=(2x)/(3)

Multiply each term in the equation by 3.
(x)/(3)*3+(2)/(7)*3-(1)/(4)*3=(2x)/(3)*3

Cancel the common factor of 3 in the denominator of the first term (x)/(3) and the second term 3.
(x)/(<X>3<x>)*<X>3<x>+(2)/(7)*3-(1)/(4)*3=(2x)/(3)*3

Reduce the expression by removing the common factor of 3 in the denominator of the first term (x)/(3) and the second term 3.
x*1+(2)/(7)*3-(1)/(4)*3=(2x)/(3)*3

Multiply x by 1 to get x.
x+(2)/(7)*3-(1)/(4)*3=(2x)/(3)*3

Multiply 2 by 3 to get 6.
x+(6)/(7)-(1)/(4)*3=(2x)/(3)*3

Multiply -1 by 3 to get -3.
x+(6)/(7)-(3)/(4)=(2x)/(3)*3

Cancel the common factor of 3 in the denominator of the first term (2x)/(3) and the second term 3.
x+(6)/(7)-(3)/(4)=(2x)/(<X>3<x>)*<X>3<x>

Reduce the expression by removing the common factor of 3 in the denominator of the first term (2x)/(3) and the second term 3.
x+(6)/(7)-(3)/(4)=2x*1

Multiply 2x by 1 to get 2x.
x+(6)/(7)-(3)/(4)=2x

Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.
x+(6)/(7)-(3)/(4)-2x=0

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both x and -2x.
(1-2)x+(6)/(7)-(3)/(4)=0

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of 1 and -2 and give the result the same sign as the integer with the greater absolute value.
(-1)x+(6)/(7)-(3)/(4)=0

Remove the parentheses.
-x+(6)/(7)-(3)/(4)=0

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 28. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-x-(3)/(4)*(7)/(7)+(6)/(7)*(4)/(4)=0

Multiply -3 by 7 to get -21.
-x-(21)/(7*4)+(6)/(7)*(4)/(4)=0

Multiply 4 by 7 to get 28.
-x-(21)/(28)+(6)/(7)*(4)/(4)=0

Multiply 6 by 4 to get 24.
-x-(21)/(28)+(24)/(4*7)=0

Multiply 7 by 4 to get 28.
-x-(21)/(28)+(24)/(28)=0

Combine the numerators of all fractions that have common denominators.
-x+(-21+24)/(28)=0

Add 24 to -21 to get 3.
-x+(3)/(28)=0

Since (3)/(28) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (3)/(28) from both sides.
-x=-(3)/(28)

Multiply each term in the equation by -1.
-x*-1=-(3)/(28)*-1

Multiply -x by -1 to get x.
x=-(3)/(28)*-1

Multiply -3 by -1 to get 3.
x=(3)/(28)