m-(m-1)/(2)=1-(m-2)/(3)

Write Equation: Write down the equation. We have the equation m - (m - 1)/2 = 1 - (m - 2)/3.Find Common Denominator: Find a common denominator for the fractions. The common denominator for 2 and 3 is 6. We will multiply each term by 6 to eliminate the fractions. 6 * [m - (m - 1)/2] = 6 * [1 - (m - 2)/3]Distribute and Eliminate Fractions: Distribute the 6 to each term. 6m - 3(m - 1) = 6 - 2(m - 2)Simplify Equations: Simplify each side of the equation. 6m - 3m + 3 = 6 - 2m + 4Combine Like Terms: Combine like terms. 3m + 3 = 10 - 2mAdd/Subtract Terms: Add 2m to both sides to get all m terms on one side. 3m + 2m + 3 = 10Combine Like Terms Again: Combine like terms again. 5m + 3 = 10Solve for m: Subtract 3 from both sides to solve for m. 5m = 10 - 3Simplify Right Side: Simplify the right side of the equation. 5m = 7Divide to Find m: Divide both sides by 5 to find the value of m. m = 7/5

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Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

m-\frac{m-1}{2}=1-\frac{m-2}{3}

Write Equation: Write down the equation. $\newline$ We have the equation $m - \frac{m - 1}{2} = 1 - \frac{m - 2}{3}$ .
Find Common Denominator: Find a common denominator for the fractions. $\newline$ The common denominator for $2$ and $3$ is $6$ . We will multiply each term by $6$ to eliminate the fractions. $\newline$ $6 \times [m - (m - 1)/2] = 6 \times [1 - (m - 2)/3]$
Distribute and Eliminate Fractions: Distribute the $6$ to each term. $\newline$ $6m - 3(m - 1) = 6 - 2(m - 2)$
Simplify Equations: Simplify each side of the equation. $\newline$ $6m - 3m + 3 = 6 - 2m + 4$
Combine Like Terms: Combine like terms. $3m + 3 = 10 - 2m$
Add/Subtract Terms: Add $2m$ to both sides to get all $m$ terms on one side. $\newline$ $3m + 2m + 3 = 10$
Combine Like Terms Again: Combine like terms again. $5m + 3 = 10$
Solve for $m$ : Subtract $3$ from both sides to solve for $m$ . $\newline$ $5m = 10 - 3$
Simplify Right Side: Simplify the right side of the equation. $5m = 7$
Divide to Find $m$ : Divide both sides by $5$ to find the value of $m$ . $m = \frac{7}{5}$