Question 345383: 2/3x+1.3=.4x+2
and
2x+7/3=5x-10/11
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (2)/(3)*x+1.3=0.4x+2
Multiply (2)/(3) by x to get (2x)/(3).
(2x)/(3)+1.3=0.4x+2
Since 0.4x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 0.4x from both sides.
(2x)/(3)+1.3-0.4x=2
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 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-0.4x*(3)/(3)+(2x)/(3)+1.3=2
Complete the multiplication to produce a denominator of 3 in each expression.
-(1.2x)/(3)+(2x)/(3)+1.3=2
Combine the numerators of all expressions that have common denominators.
(-1.2x+2x)/(3)+1.3=2
Combine all like terms in the numerator.
(0.8x)/(3)+1.3=2
Reduce the expression (0.8x)/(3) by removing a factor of from the numerator and denominator.
0.27x+1.3=2
Since 1.3 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1.3 from both sides.
0.27x=-1.3+2
Add 2 to -1.3 to get 0.7.
0.27x=0.7
Divide each term in the equation by 0.27.
(0.27x)/(0.27)=(0.7)/(0.27)
Cancel the common factor of 0.27.
x=(0.7)/(0.27)
Divide 0.7 by 0.27 to get 2.62.
x=2.62
2x+(7)/(3)=5x-(10)/(11)
Since 5x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 5x from both sides.
2x+(7)/(3)-5x=-(10)/(11)
Since 2x and -5x are like terms, add -5x to 2x to get -3x.
-3x+(7)/(3)=-(10)/(11)
Since (7)/(3) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (7)/(3) from both sides.
-3x=-(7)/(3)-(10)/(11)
Simplify the right-hand side of the equation.
-3x=-(107)/(33)
Divide each term in the equation by -3.
-(3x)/(-3)=-(107)/(33)*-(1)/(3)
Simplify the left-hand side of the equation by canceling the common factors.
x=-(107)/(33)*-(1)/(3)
Simplify the right-hand side of the equation by simplifying each term.
x=(107)/(99)
|
|
|
