Solve the following equation for w. {:[sqrt(5-(w)/(4))=sqrt(w+8)],[w=]:}

Given equation: We are given the equation: sqrt(5 - w/4) = sqrt(w + 8) To solve for w, we need to isolate w on one side of the equation. The first step is to remove the square roots by squaring both sides of the equation.Step 1: Remove square roots: Square both sides of the equation: (sqrt(5 - w/4))^2 = (sqrt(w + 8))^2 This simplifies to: 5 - w/4 = w + 8Step 2: Simplify the equation: Now, we need to get all the w terms on one side and the constant terms on the other side. Let's move the w terms to the left side and the constants to the right side by adding w/4 to both sides and subtracting 8 from both sides: 5 - w/4 + w/4 = w + 8 + w/4 - 8 This simplifies to: 5 = w + w/4Step 3: Rearrange the equation: To combine the w terms, we need a common denominator. The common denominator is 4, so we rewrite w as 4w/4: 5 = 4w/4 + w/4 This simplifies to: 5 = (4w + w)/4Step 4: Combine like terms: Now, multiply both sides by 4 to get rid of the denominator: 4 * 5 = (4w + w) This simplifies to: 20 = 5wStep 5: Multiply both sides: Finally, divide both sides by 5 to solve for w: 20 / 5 = 5w / 5 This simplifies to: 4 = w

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Algebra 1

Domain and range of square root functions: equations

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Q. Solve the following equation for

w

\newline

\begin{array}{l} \sqrt{5-\frac{w}{4}}=\sqrt{w+8} \\ w= \end{array}

Given equation: We are given the equation: $\newline$ $\sqrt{5 - \frac{w}{4}} = \sqrt{w + 8}$ $\newline$ To solve for $w$ , we need to isolate $w$ on one side of the equation. The first step is to remove the square roots by squaring both sides of the equation.
Step $1$ : Remove square roots: Square both sides of the equation: $\newline$ $(\sqrt{5 - \frac{w}{4}})^2 = (\sqrt{w + 8})^2$ $\newline$ This simplifies to: $\newline$ $5 - \frac{w}{4} = w + 8$
Step $2$ : Simplify the equation: Now, we need to get all the $w$ terms on one side and the constant terms on the other side. Let's move the $w$ terms to the left side and the constants to the right side by adding $\frac{w}{4}$ to both sides and subtracting $8$ from both sides: $\newline$ $5 - \frac{w}{4} + \frac{w}{4} = w + 8 + \frac{w}{4} - 8$ $\newline$ This simplifies to: $\newline$ $5 = w + \frac{w}{4}$
Step $3$ : Rearrange the equation: To combine the $w$ terms, we need a common denominator. The common denominator is $4$ , so we rewrite $w$ as $\frac{4w}{4}$ : $\newline$ $5 = \frac{4w}{4} + \frac{w}{4}$ $\newline$ This simplifies to: $\newline$ $5 = \frac{(4w + w)}{4}$
Step $4$ : Combine like terms: Now, multiply both sides by $4$ to get rid of the denominator: $\newline$ $4 \times 5 = (4w + w)$ $\newline$ This simplifies to: $\newline$ $20 = 5w$
Step $5$ : Multiply both sides: Finally, divide both sides by $5$ to solve for $w$ : $\frac{20}{5} = \frac{5w}{5}$ This simplifies to: $4 = w$