Solve the equation (2x+7)/(3)=(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 * 12 = (2 - x)/4 * 12Distribute Terms: Now we distribute 12 to the terms on both sides of the equation. (2x + 7) * 4 = (2 - x) * 3 8x + 28 = 6 - 3xCombine 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 - 28Solve for x: Now we combine like terms on both sides of the equation. 11x = -22Finally, we solve for x by dividing both sides of the equation by 11. 11x / 11 = -22 / 11 x = -2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

Home

Math Problems

Grade 8

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 $11$ . $\newline$ $\frac{11x}{11} = \frac{-22}{11}$ $\newline$ $x = -2$