Question

solve the equation $\frac{2x - 1}{5}=\frac{3x + 1}{10}$ by arranging the steps in the correct order
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$10(2x - 1)=5(3x + 1)$ $20x-15x - 10=15x - 15x + 5$ $5x - 10 + 10=5 + 10$ $\frac{2x - 1}{5}=\frac{3x + 1}{10}$ $x = 3$ $20x-10 = 15x + 5$ $5x - 10=5$ $5x=15$

Explanation:

Step1: Cross - multiply

$10(2x - 1)=5(3x + 1)$

Step2: Expand both sides

$20x-10 = 15x + 5$

Step3: Subtract 15x from both sides

$20x-15x - 10=15x-15x + 5$

Step4: Simplify the left - hand side

$5x-10 = 5$

Step5: Add 10 to both sides

$5x-10 + 10=5 + 10$

Step6: Simplify both sides

$5x=15$

Step7: Divide both sides by 5

$\frac{5x}{5}=\frac{15}{5}$

Step8: Simplify to get the solution

$x = 3$

Answer:

Line 1: $\frac{2x - 1}{5}=\frac{3x + 1}{10}$
Line 2: $10(2x - 1)=5(3x + 1)$
Line 3: $20x-10 = 15x + 5$
Line 4: $20x-15x - 10=15x-15x + 5$
Line 5: $5x-10 = 5$
Line 6: $5x-10 + 10=5 + 10$
Line 7: $5x=15$
Line 8: $\frac{5x}{5}=\frac{15}{5}$
Line 9: $x = 3$