Distribute 3x: Distribute the 3x across the terms inside the parentheses. 3x * (10/2) + 3x * (x/2) = 15xSimplify multiplication: Simplify the multiplication inside the parentheses. 3x * 5 + 3x * (1/2)x = 15xContinue simplifying: Continue simplifying the equation. 15x + (3/2)x^2 = 15xSubtract 15x: Subtract 15x from both sides to move all terms involving x to one side. 15x + (3/2)x^2 - 15x = 15x - 15xSimplify equation: Simplify both sides of the equation. (3/2)x^2 = 0Conclude x=0: Since (3/2)x^2 = 0, we can conclude that x must be 0 for the equation to hold true. x = 0

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$3x\left(\frac{10+x}{2}\right)=15x$

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Math Problems

Algebra 1

Add and subtract polynomials

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3x\left(\frac{10+x}{2}\right)=15x

Distribute $3x$ : Distribute the $3x$ across the terms inside the parentheses. $\newline$ $3x \times (\frac{10}{2}) + 3x \times (\frac{x}{2}) = 15x$
Simplify multiplication: Simplify the multiplication inside the parentheses. $3x \times 5 + 3x \times (\frac{1}{2})x = 15x$
Continue simplifying: Continue simplifying the equation. $15x + \left(\frac{3}{2}\right)x^2 = 15x$
Subtract $15x$ : Subtract $15x$ from both sides to move all terms involving $x$ to one side. $\newline$ $15x + \left(\frac{3}{2}\right)x^2 - 15x = 15x - 15x$
Simplify equation: Simplify both sides of the equation. $\newline$ $(\frac{3}{2})x^2 = 0$
Conclude $x=0$ : Since $\frac{3}{2}x^2 = 0$ , we can conclude that $x$ must be $0$ for the equation to hold true. $\newline$ $x = 0$