Solve for x. (x+1)/(2)=(x+3)/(3)

Find Common Denominator: To solve the equation (x+1)/2 = (x+3)/3, we need to find a common denominator to combine the fractions. The common denominator for 2 and 3 is 6. We will multiply both sides of the equation by 6 to eliminate the denominators. 6 * (x+1)/2 = 6 * (x+3)/3Multiply by 6: After multiplying both sides by 6, we distribute the 6 to the numerators on both sides of the equation. (6 * (x+1))/2 = (6 * (x+3))/3 This simplifies to: 3 * (x+1) = 2 * (x+3)Distribute 6: Now we distribute the 3 and the 2 into the parentheses. 3x + 3 = 2x + 6Distribute 3 and 2: Next, we want to get all the x terms on one side and the constants on the other side. We can do this by subtracting 2x from both sides and subtracting 3 from both sides. 3x + 3 - 2x - 3 = 2x + 6 - 2x - 3Combine Like Terms: Simplifying both sides of the equation gives us: x = 3

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Solve for $x$ . $\newline$ $\frac{x+1}{2}=\frac{x+3}{3}$

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Math Problems

Grade 7

Add and subtract linear expressions

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Q. Solve for

x

\newline

\frac{x+1}{2}=\frac{x+3}{3}

Find Common Denominator: To solve the equation $(x+1)/2 = (x+3)/3$ , we need to find a common denominator to combine the fractions. The common denominator for $2$ and $3$ is $6$ . We will multiply both sides of the equation by $6$ to eliminate the denominators. $\newline$ $6 \times (x+1)/2 = 6 \times (x+3)/3$
Multiply by $6$ : After multiplying both sides by $6$ , we distribute the $6$ to the numerators on both sides of the equation. $\newline$ $\frac{6 \times (x+1)}{2} = \frac{6 \times (x+3)}{3}$ $\newline$ This simplifies to: $\newline$ $3 \times (x+1) = 2 \times (x+3)$
Distribute $6$ : Now we distribute the $3$ and the $2$ into the parentheses. $\newline$ $3x + 3 = 2x + 6$
Distribute $3$ and $2$ : Next, we want to get all the $x$ terms on one side and the constants on the other side. We can do this by subtracting $2x$ from both sides and subtracting $3$ from both sides. $\newline$ $3x + 3 - 2x - 3 = 2x + 6 - 2x - 3$
Combine Like Terms: Simplifying both sides of the equation gives us: $\newline$ $x = 3$