Distribute numbers to terms: Distribute the numbers outside the parentheses to the terms inside. Calculate 3(x-2) and 2(3-x). 3(x-2) = 3*x - 3*2 = 3x - 6 2(3-x) = 2*3 - 2*x = 6 - 2xWrite with distributed terms: Write the equation with the distributed terms. Combine the results from Step 1 into the equation. 3x - 6 + 6 - 2x = 1Combine distributed terms: Combine like terms on the left side of the equation. Add (3x - 2x) and (-6 + 6). 3x - 2x = x -6 + 6 = 0 So, x + 0 = 1Combine like terms: Simplify the equation. Since -6 + 6 is 0, it cancels out, leaving x on the left side. x = 1

Grade 8

Solve equations with the distributive property

Full solution

3(x-2)+2(3-x)=1

Distribute numbers to terms: Distribute the numbers outside the parentheses to the terms inside. $\newline$ Calculate $3(x-2)$ and $2(3-x)$ . $\newline$ $3(x-2) = 3\times x - 3\times 2 = 3x - 6$ $\newline$ $2(3-x) = 2\times 3 - 2\times x = 6 - 2x$
Write with distributed terms: Write the equation with the distributed terms. $\newline$ Combine the results from Step $1$ into the equation. $\newline$ $3x - 6 + 6 - 2x = 1$
Combine distributed terms: Combine like terms on the left side of the equation. $\newline$ Add $(3x - 2x)$ and $(-6 + 6)$ . $\newline$ $3x - 2x = x$ $\newline$ $-6 + 6 = 0$ $\newline$ So, $x + 0 = 1$
Combine like terms: Simplify the equation. $\newline$ Since $-6 + 6$ is $0$ , it cancels out, leaving $x$ on the left side. $\newline$ $x = 1$