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Question Solve the equation −5m(x)=−3x+4+5-5 m(x)=-3 \sqrt{x+4}+5 for m(x)m(x).

Studdy Solution

STEP 1

1. The function m(x)m(x) is a real-valued function of the real variable xx.
2. The square root function, x+4\sqrt{x+4}, is defined for x+4≥0x+4 \geq 0, which implies that x≥−4x \geq -4.
3. The equation −5m(x)=−3x+4+5-5 m(x)=-3 \sqrt{x+4}+5 can be solved for m(x)m(x) by algebraic manipulation.

STEP 2

1. Isolate the function m(x)m(x) on one side of the equation.
2. Solve for m(x)m(x) by dividing both sides of the equation by the coefficient of m(x)m(x).

STEP 3

Add 3x+43 \sqrt{x+4} to both sides of the equation to isolate terms involving m(x)m(x).
−5m(x)+3x+4=5+3x+4 -5 m(x) + 3 \sqrt{x+4} = 5 + 3 \sqrt{x+4}

STEP 4

Simplify the right-hand side of the equation.
−5m(x)+3x+4=5+3x+4 -5 m(x) + 3 \sqrt{x+4} = 5 + 3 \sqrt{x+4}

STEP 5

Divide both sides of the equation by −5-5 to solve for m(x)m(x).
m(x)=−5−3x+4−5 m(x) = \frac{-5 - 3 \sqrt{x+4}}{-5}

STEP 6

Simplify the right-hand side of the equation by dividing each term by −5-5.
m(x)=1+35x+4 m(x) = 1 + \frac{3}{5} \sqrt{x+4}
The solution for m(x)m(x) is:
m(x)=1+35x+4 m(x) = 1 + \frac{3}{5} \sqrt{x+4}

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