please solve the problem and help
Answers
Answer:
-8/7
Step-by-step explanation:
By cross multiplication
=> 10(2x + 1) = 9(3x + 2)
=> 20x + 10 = 27x + 18
=> 27x - 20x = 10 - 18
=> 7x = - 8
=> x = - 8/7
Answer:
Multiply all terms by the same value to eliminate fraction denominators
2+13+2=910
\frac{2x+1}{3x+2}=\frac{9}{10}
(3+2)⋅2+13+2=(3+2)⋅910
(3x+2) \cdot \frac{2x+1}{3x+2}=(3x+2) \cdot \frac{9}{10}
2
Cancel multiplied terms that are in the denominator
(3+2)⋅2+13+2=(3+2)⋅910
(3x+2) \cdot \frac{2x+1}{3x+2}=(3x+2) \cdot \frac{9}{10}
2+1=(3+2)⋅910
2x+1=(3x+2) \cdot \frac{9}{10}
3
Re-order terms so that constants are on the left
2+1=(3+2)⋅910
2x+1=(3x+2) \cdot {\color{#c92786}{\frac{9}{10}}}
2+1=910(3+2)
2x+1={\color{#c92786}{\frac{9}{10}}}(3x+2)
4
Combine multiplied terms into a single fraction
2+1=910(3+2)
2x+1=\frac{9}{10}(3x+2)
2+1=9(3+2)10
2x+1=\frac{9(3x+2)}{10}
5
Distribute
2+1=9(3+2)10
2x+1=\frac{{\color{#c92786}{9(3x+2)}}}{10}
2+1=27+1810
2x+1=\frac{{\color{#c92786}{27x+18}}}{10}
6
Subtract
1
1
from both sides of the equation
2+1=27+1810
2x+1=\frac{27x+18}{10}
2+1−1=27+1810−1
2x+1{\color{#c92786}{-1}}=\frac{27x+18}{10}{\color{#c92786}{-1}}
7
Simplify
Subtract the numbers
Find common denominator
Combine fractions with common denominator
Multiply the numbers
Subtract the numbers
2=27+810
2x=\frac{27x+8}{10}
8
Multiply all terms by the same value to eliminate fraction denominators
2=27+810
2x=\frac{27x+8}{10}
10⋅2=10⋅27+810
10 \cdot 2x=10 \cdot \frac{27x+8}{10}
9
Cancel multiplied terms that are in the denominator
10⋅2=10⋅27+810
10 \cdot 2x=10 \cdot \frac{27x+8}{10}
10⋅2=27+8
10 \cdot 2x=27x+8
10
Multiply the numbers
10⋅2=27+8
{\color{#c92786}{10}} \cdot {\color{#c92786}{2}}x=27x+8
20=27+8
{\color{#c92786}{20}}x=27x+8
11
Subtract
27
27x
from both sides of the equation
20=27+8
20x=27x+8
20−27=27+8−27
20x{\color{#c92786}{-27x}}=27x+8{\color{#c92786}{-27x}}
12