Solve for x. (x-3)/(2)+(x+1)/(5)=x-4 Answer:

Find Common Denominator: Find a common denominator for the fractions and combine them into a single fraction. The common denominator for 2 and 5 is 10. Multiply each term by 10 to eliminate the denominators. 10 * (x-3)/2 + 10 * (x+1)/5 = 10 * (x-4) 5(x-3) + 2(x+1) = 10(x-4)Multiply and Combine Fractions: Distribute the multiplication across the parentheses. 5x - 15 + 2x + 2 = 10x - 40Distribute Multiplication: Combine like terms on the left side of the equation. 5x + 2x - 15 + 2 = 10x - 40 7x - 13 = 10x - 40Combine Like Terms: Move all terms containing x to one side and constant terms to the other side. 7x - 10x = -40 + 13 -3x = -27Move Terms and Constants: Divide both sides by -3 to solve for x. -3x / -3 = -27 / -3 x = 9

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Solve for
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(x-3)/(2)+(x+1)/(5)=x-4
Answer:

Solve for $\mathrm{x}$ . $\newline$ $\frac{x-3}{2}+\frac{x+1}{5}=x-4$ $\newline$ Answer:

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Math Problems

Grade 8

Solve equations with the distributive property

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Q. Solve for

\mathrm{x}

\newline

\frac{x-3}{2}+\frac{x+1}{5}=x-4

\newline

Answer:

Find Common Denominator: Find a common denominator for the fractions and combine them into a single fraction. $\newline$ The common denominator for $2$ and $5$ is $10$ . Multiply each term by $10$ to eliminate the denominators. $\newline$ $10 \times \frac{x-3}{2} + 10 \times \frac{x+1}{5} = 10 \times (x-4)$ $\newline$ $5(x-3) + 2(x+1) = 10(x-4)$
Multiply and Combine Fractions: Distribute the multiplication across the parentheses. $5x - 15 + 2x + 2 = 10x - 40$
Distribute Multiplication: Combine like terms on the left side of the equation. $\newline$ $5x + 2x - 15 + 2 = 10x - 40$ $\newline$ $7x - 13 = 10x - 40$
Combine Like Terms: Move all terms containing $x$ to one side and constant terms to the other side. $7x - 10x = -40 + 13$ $-3x = -27$
Move Terms and Constants: Divide both sides by $-3$ to solve for $x$ . $\frac{-3x}{-3} = \frac{-27}{-3}$ $x = 9$