Solve for m. sqrt ( 4 + 5m) = sqrt 9m m = _____

Set Equal Square Roots: Set the expressions inside the square roots equal to each other since the square roots are equal. √(4 + 5m) = √9m 4 + 5m = 9m Isolate Variable m: Isolate the variable m by moving all terms involving m to one side of the equation. 4 + 5m - 9m = 9m - 9m 4 - 4m = 0 Move Constant Term: Move the constant term to the other side of the equation to solve for m. 4 - 4m = 0 -4m = -4 Divide by -4: Divide both sides of the equation by -4 to solve for m. -4m / -4 = -4 / -4 m = 1

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Math Problems

Grade 8

Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for

m

\newline

\sqrt{4 + 5m} = \sqrt{9m}

\newline

m =

_____

Set Equal Square Roots: Set the expressions inside the square roots equal to each other since the square roots are equal. $\newline$ $\sqrt{4 + 5m} = \sqrt{9m}$ $\newline$ $4 + 5m = 9m$
Isolate Variable $m$ : Isolate the variable $m$ by moving all terms involving $m$ to one side of the equation. $\newline$ $4 + 5m - 9m = 9m - 9m$ $\newline$ $4 - 4m = 0$
Move Constant Term: Move the constant term to the other side of the equation to solve for $m$ . $4 - 4m = 0$ $-4m = -4$
Divide by $-4$ : Divide both sides of the equation by $-4$ to solve for m. $\newline$ $-4m / -4 = -4 / -4$ $\newline$ $m = 1$