9x-(9)/(2)*(x-5)=45
Multiply the rational expressions to get -(9(x-5))/(2).
9x-(9(x-5))/(2)=45
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 2.
9x*(2)/(2)-(9(x-5))/(2)=45
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 2.
(9x*2)/(2)-(9(x-5))/(2)=45
Multiply 9x by 2 to get 18x.
(18x)/(2)-(9(x-5))/(2)=45
The numerators of expressions that have equal denominators can be combined. In this case, ((18x))/(2) and -(9(x-5))/(2) have the same denominator of 2, so the numerators can be combined.
((18x)-9(x-5))/(2)=45
Remove the parentheses around the expression 18x.
(18x-9(x-5))/(2)=45
Multiply -9 by each term inside the parentheses (x-5).
(18x-9(x)-9(-5))/(2)=45
Multiply -9 by the x inside the parentheses.
(18x-9*x-9(-5))/(2)=45
Multiply -9 by x to get -9x.
(18x-9x-9(-5))/(2)=45
Multiply -9 by the -5 inside the parentheses.
(18x-9x-9*-5)/(2)=45
Multiply -9 by -5 to get 45.
(18x-9x+45)/(2)=45
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 18x and -9x.
((18-9)x+45)/(2)=45
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 18 and -9 and give the result the same sign as the integer with the greater absolute value.
((9)x+45)/(2)=45
Remove the parentheses.
(9x+45)/(2)=45
Factor out the GCF of 9 from the expression 9x.
(9(x)+45)/(2)=45
Factor out the GCF of 9 from the expression 45.
(9(x)+9(5))/(2)=45
Factor out the GCF of 9 from 9x+45.
(9(x+5))/(2)=45
Multiply each term in the equation by 2.
(9(x+5))/(2)*2=45*2
Cancel the common factor of 2 from the denominator of the first expression and the numerator of the second expression.
(9(x+5))/(2)*2=45*2
Cancel the common factor of 2 from the denominator of the first expression and the numerator of the second expression.
9(x+5)=45*2
Multiply 45 by 2 to get 90.
9(x+5)=90
Divide each term in the equation by 9.
(9(x+5))/(9)=(90)/(9)
Cancel the common factor of 9 the expression (9(x+5))/(9).
(9(x+5))/(9)=(90)/(9)
Remove the common factors that were cancelled out.
(x+5)=(90)/(9)
Remove the parentheses around the expression x+5.
x+5=(90)/(9)
Cancel the common factor of 9 in (90)/(9).
x+5=(^(10)90)/(9)
Remove the common factors that were cancelled out.
x+5=10
Since 5 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 5 from both sides.
x=-5+10
Add 10 to -5 to get 5.
x=5