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Solve the equation (2x+7)/(3)=(2-x)/(4).

Solve the equation $\frac{2 x+7}{3}=\frac{2-x}{4}$ .

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Solve multi-step equations with fractional coefficients

Full solution

Q. Solve the equation

\frac{2 x+7}{3}=\frac{2-x}{4}

.

Eliminate Fractions: First, we need to eliminate the fractions by finding a common denominator and then multiplying both sides of the equation by that common denominator. The common denominator for $3$ and $4$ is $12$ . So we multiply both sides of the equation by $12$ to get rid of the denominators. $(2x + 7)/3 \times 12 = (2 - x)/4 \times 12$
Distribute Terms: Now we distribute $12$ to the terms on both sides of the equation. $\newline$ $(2x + 7) \times 4 = (2 - x) \times 3$ $\newline$ $8x + 28 = 6 - 3x$
Combine Like Terms: Next, we want to get all the $x$ terms on one side and the constant terms on the other side. We can do this by adding $3x$ to both sides and subtracting $28$ from both sides. $8x + 28 + 3x = 6 - 3x + 3x$ $8x + 3x + 28 - 28 = 6 - 28$
Solve for x: Now we combine like terms on both sides of the equation. $\newline$ $11x = -22$
Solve for x: Now we combine like terms on both sides of the equation. $\newline$ $11x = -22$ Finally, we solve for x by dividing both sides of the equation by $11$ . $\newline$ $\frac{11x}{11} = \frac{-22}{11}$ $\newline$ $x = -2$

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