Solve 2/9(3x-5)=3/2(5-3x)
Answers
Answer:
5/3
Step-by-step explanation:
How to solve your problem
2
9
(
3
−
5
)
=
3
2
(
5
−
3
)
\frac{2}{9}(3x-5)=\frac{3}{2}(5-3x)
92(3x−5)=23(5−3x)
Solve
1
Combine multiplied terms into a single fraction
2
9
(
3
−
5
)
=
3
2
(
5
−
3
)
\frac{2}{9}(3x-5)=\frac{3}{2}(5-3x)
92(3x−5)=23(5−3x)
2
(
3
−
5
)
9
=
3
2
(
5
−
3
)
\frac{2(3x-5)}{9}=\frac{3}{2}(5-3x)
92(3x−5)=23(5−3x)
2
Distribute
2
(
3
−
5
)
9
=
3
2
(
5
−
3
)
\frac{{\color{#c92786}{2(3x-5)}}}{9}=\frac{3}{2}(5-3x)
92(3x−5)=23(5−3x)
6
−
1
0
9
=
3
2
(
5
−
3
)
\frac{{\color{#c92786}{6x-10}}}{9}=\frac{3}{2}(5-3x)
96x−10=23(5−3x)
3
Rearrange terms
6
−
1
0
9
=
3
2
(
5
−
3
)
\frac{6x-10}{9}=\frac{3}{2}({\color{#c92786}{5-3x}})
96x−10=23(5−3x)
6
−
1
0
9
=
3
2
(
−
3
+
5
)
\frac{6x-10}{9}=\frac{3}{2}({\color{#c92786}{-3x+5}})
96x−10=23(−3x+5)
4
Combine multiplied terms into a single fraction
6
−
1
0
9
=
3
2
(
−
3
+
5
)
\frac{6x-10}{9}=\frac{3}{2}(-3x+5)
96x−10=23(−3x+5)
6
−
1
0
9
=
3
(
−
3
+
5
)
2
\frac{6x-10}{9}=\frac{3(-3x+5)}{2}
96x−10=23(−3x+5)
5
Distribute
6
−
1
0
9
=
3
(
−
3
+
5
)
2
\frac{6x-10}{9}=\frac{{\color{#c92786}{3(-3x+5)}}}{2}
96x−10=23(−3x+5)
6
−
1
0
9
=
−
9
+
1
5
2
\frac{6x-10}{9}=\frac{{\color{#c92786}{-9x+15}}}{2}
96x−10=2−9x+15
6
Multiply all terms by the same value to eliminate fraction denominators
6
−
1
0
9
=
−
9
+
1
5
2
\frac{6x-10}{9}=\frac{-9x+15}{2}
96x−10=2−9x+15
1
8
⋅
6
−
1
0
9
=
1
8
(
−
9
+
1
5
2
)
18 \cdot \frac{6x-10}{9}=18(\frac{-9x+15}{2})
18⋅96x−10=18(2−9x+15)
7
Cancel multiplied terms that are in the denominator
1
8
⋅
6
−
1
0
9
=
1
8
(
−
9
+
1
5
2
)
18 \cdot \frac{6x-10}{9}=18(\frac{-9x+15}{2})
18⋅96x−10=18(2−9x+15)
2
(
6
−
1
0
)
=
9
(
−
9
+
1
5
)
2(6x-10)=9(-9x+15)
2(6x−10)=9(−9x+15)
8
Distribute
2
(
6
−
1
0
)
=
9
(
−
9
+
1
5
)
{\color{#c92786}{2(6x-10)}}=9(-9x+15)
2(6x−10)=9(−9x+15)
1
2
−
2
0
=
9
(
−
9
+
1
5
)
{\color{#c92786}{12x-20}}=9(-9x+15)
12x−20=9(−9x+15)
9
Distribute
1
2
−
2
0
=
9
(
−
9
+
1
5
)
12x-20={\color{#c92786}{9(-9x+15)}}
12x−20=9(−9x+15)
1
2
−
2
0
=
−
8
1
+
1
3
5
12x-20={\color{#c92786}{-81x+135}}
12x−20=−81x+135
10
Add
2
0
20
20
to both sides of the equation
1
2
−
2
0
=
−
8
1
+
1
3
5
12x-20=-81x+135
12x−20=−81x+135
1
2
−
2
0
+
2
0
=
−
8
1
+
1
3
5
+
2
0
12x-20+{\color{#c92786}{20}}=-81x+135+{\color{#c92786}{20}}
12x−20+20=−81x+135+20
11
Simplify
Add the numbers
Add the numbers
1
2
=
−
8
1
+
1
5
5
12x=-81x+155
12x=−81x+155
12
Add
8
1
81x
81x
to both sides of the equation
1
2
=
−
8
1
+
1
5
5
12x=-81x+155
12x=−81x+155
1
2
+
8
1
=
−
8
1
+
1
5
5
+
8
1
12x+{\color{#c92786}{81x}}=-81x+155+{\color{#c92786}{81x}}
12x+81x=−81x+155+81x
13
Simplify
Combine like terms
Combine like terms
9
3
=
1
5
5
93x=155
93x=155
14
Divide both sides of the equation by the same term
9
3
=
1
5
5
93x=155
93x=155
9
3
9
3
=
1
5
5
9
3
\frac{93x}{{\color{#c92786}{93}}}=\frac{155}{{\color{#c92786}{93}}}
9393x=93155
15
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
=
5
3
x=\frac{5}{3}
x=35
Show less
Solution
=
5
3
Answer:
2/9(3x-5) =3/2(5-3x)
6x/9-10/9=15/2-9x/2
6x/9+9x/2=15/2+10/9
12x+81x/18=135+20/18
93x/18=165/18
X=18×165/93×18
X=55/31