Question

b. solve xavier’s equation using two different methods.
show and explain all your steps. the two different methods may include the same
operations, but in a different order. try to make the methods as different as possible.

1. solve the following equation. show and explain all your steps.

\\(\frac{5x - 8}{3} + 10 = 19\\)

Explanation:

Method 1: Isolate the fraction first

1. Subtract 10 from both sides: $\frac{5x - 8}{3}+10 - 10=19 - 10$

Simplifies to: $\frac{5x - 8}{3}=9$

1. Multiply both sides by 3: $3\times\frac{5x - 8}{3}=9\times3$

Simplifies to: $5x - 8 = 27$

1. Add 8 to both sides: $5x - 8+8 = 27+8$

Simplifies to: $5x = 35$

1. Divide by 5: $\frac{5x}{5}=\frac{35}{5}$

Simplifies to: $x = 7$

Method 2: Eliminate the denominator first

1. Multiply every term by 3: $3\times\frac{5x - 8}{3}+3\times10 = 3\times19$

Simplifies to: $5x - 8+30 = 57$

1. Combine like terms: $5x + 22 = 57$
2. Subtract 22: $5x + 22 - 22 = 57 - 22$

Simplifies to: $5x = 35$

1. Divide by 5: $\frac{5x}{5}=\frac{35}{5}$

Simplifies to: $x = 7$

Answer:

The solution to the equation $\frac{5x - 8}{3}+10 = 19$ is $x = 7$.