Solve (x)/(2)-4=(x)/(3)+2

Clear Fractions: Clear the fractions by finding a common denominator for the terms involving x. The common denominator for 2 and 3 is 6. Multiply every term in the equation by 6 to eliminate the fractions. 6 * ((x)/(2) - 4) = 6 * ((x)/(3) + 2)Distribute 6: Distribute 6 to the terms in both sides of the equation. 6 * (x/2) - 6 * 4 = 6 * (x/3) + 6 * 2 3x - 24 = 2x + 12Isolate Variables: Isolate the variable terms on one side and the constant terms on the other side. Subtract 2x from both sides to move the x terms to the left side. 3x - 2x - 24 = 2x - 2x + 12 x - 24 = 12Solve for x: Solve for x by isolating it on one side. Add 24 to both sides to move the constant term to the right side. x - 24 + 24 = 12 + 24 x = 36

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Math Problems

Grade 8

Solve multi-step equations with fractional coefficients

Full solution

Q. Solve

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

Clear Fractions: Clear the fractions by finding a common denominator for the terms involving $x$ . The common denominator for $2$ and $3$ is $6$ . Multiply every term in the equation by $6$ to eliminate the fractions. $6 \times \left(\frac{x}{2} - 4\right) = 6 \times \left(\frac{x}{3} + 2\right)$
Distribute $6$ : Distribute $6$ to the terms in both sides of the equation. $\newline$ $6 \times (x/2) - 6 \times 4 = 6 \times (x/3) + 6 \times 2$ $\newline$ $3x - 24 = 2x + 12$
Isolate Variables: Isolate the variable terms on one side and the constant terms on the other side. $\newline$ Subtract $2x$ from both sides to move the $x$ terms to the left side. $\newline$ $3x - 2x - 24 = 2x - 2x + 12$ $\newline$ $x - 24 = 12$
Solve for x: Solve for x by isolating it on one side. $\newline$ Add $24$ to both sides to move the constant term to the right side. $\newline$ $x - 24 + 24 = 12 + 24$ $\newline$ $x = 36$