Verified answer

Answer:

[tex]x=\frac{20}{11}=1\frac{9}{11}[/tex]

Step-by-step explanation:

.Group like terms:

[tex]\left(7x+\frac{-3}{5}\cdot x\right)+\left(-17+\frac{14}{3}\right)=6x-4x+\frac{2}{3}-5[/tex]

Convert the integer into a fraction:

[tex]\left(\frac{35}{5}+\frac{-3}{5}\right)x+\left(-17+\frac{14}{3}\right)=6x-4x+\frac{2}{3}-5[/tex]

Combine the fractions:

[tex]\frac{\left(35-3\right)}{5}\cdot x+\left(-17+\frac{14}{3}\right)=6x-4x+\frac{2}{3}-5

[/tex]

Combine the numerators:

[tex]\frac{32}{5}\cdot x+\left(-17+\frac{14}{3}\right)=6x-4x+\frac{2}{3}-5[/tex]

Convert the integer into a fraction:

[tex]\frac{32}{5}\cdot x+\frac{-51}{3}+\frac{14}{3}=6x-4x+\frac{2}{3}-5[/tex]

Combine the fractions:

[tex]\frac{32}{5}\cdot x+\frac{\left(-51+14\right)}{3}=6x-4x+\frac{2}{3}-5[/tex]

Combine the numerators:

[tex]\frac{32}{5}\cdot x+\frac{-37}{3}=6x-4x+\frac{2}{3}-5[/tex]

Group like terms:

[tex]\frac{32}{5}\cdot x+\frac{-37}{3}=\left(6x-4x\right)+\left(-5+\frac{2}{3}\right)[/tex]

Simplify the arithmetic:

[tex]\frac{32}{5}\cdot x+\frac{-37}{3}=2x+\left(-5+\frac{2}{3}\right)[/tex]

Convert the integer into a fraction:

[tex]\frac{32}{5}\cdot x+\frac{-37}{3}=2x+\frac{-15}{3}+\frac{2}{3}[/tex]

Combine the fractions:

[tex]\frac{32}{5}\cdot x+\frac{-37}{3}=2x+\frac{\left(-15+2\right)}{3}[/tex]

Combine the numerators:

[tex]\frac{32}{5}\cdot x+\frac{-37}{3}=2x+\frac{-13}{3}[/tex]

simplyfy the last step and the answer will be

[tex]x=\frac{20}{11}=1\frac{9}{11}[/tex]

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Answer:

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