Solve for x. (x-8)/(3)-(x-9)/(5)=-3 Answer:

Find Common Denominator: Find a common denominator for the fractions to combine them. The common denominator for 3 and 5 is 15. Multiply each term by 15 to eliminate the denominators. (15 * (x-8)/3) - (15 * (x-9)/5) = 15 * -3Multiply and Eliminate: Simplify each term. (5 * (x-8)) - (3 * (x-9)) = -45 5x - 40 - 3x + 27 = -45Simplify Terms: Combine like terms. 2x - 13 = -45Combine Like Terms: Isolate the variable x. Add 13 to both sides of the equation. 2x - 13 + 13 = -45 + 13 2x = -32Isolate Variable: Divide both sides by 2 to solve for x. 2x / 2 = -32 / 2 x = -16

Home

Math Problems

Grade 8

Solve equations with the distributive property

Full solution

Q. Solve for

\mathrm{x}

\newline

\frac{x-8}{3}-\frac{x-9}{5}=-3

\newline

Answer:

Find Common Denominator: Find a common denominator for the fractions to combine them. $\newline$ The common denominator for $3$ and $5$ is $15$ . Multiply each term by $15$ to eliminate the denominators. $\newline$ $(15 \times (x-8)/3) - (15 \times (x-9)/5) = 15 \times -3$
Multiply and Eliminate: Simplify each term. $\newline$ $(5 \times (x-8)) - (3 \times (x-9)) = -45$ $\newline$ $5x - 40 - 3x + 27 = -45$
Simplify Terms: Combine like terms. $2x - 13 = -45$
Combine Like Terms: Isolate the variable $x$ . Add $13$ to both sides of the equation. $2x - 13 + 13 = -45 + 13$ $2x = -32$
Isolate Variable: Divide both sides by $2$ to solve for $x$ . $\frac{2x}{2} = \frac{-32}{2}$ $x = -16$