Question

*make sure you show your work only for the problems you were assigned. radical equations directions: solve each equation. identify matching answers between column 1 and column 2, then color the dinosaur accordingly. staple all work to this paper! column 1 1. $sqrt{3x - 17}+2 = 7$ 2. $5sqrt3{2x + 11}=15$ 3. $2=\frac{1+sqrt{29 - 4x}}{-3}$ 4. $2(12p + 28)^{\frac{1}{4}}-15=-7$ 5. $3 = 11-(4 - 6x)^{\frac{1}{2}}$ 6. $(4x + 12)^{\frac{1}{3}}+3 = 1$ 7. $sqrt{4x - 1}=sqrt{9 - x}$ 8. $sqrt4{39 - 2x}=sqrt4{2x - 9}$ 9. $sqrt{13x + 27}=4sqrt{x}$ 10. $x=sqrt{10x - 24}$ 11. $sqrt{7x + 43}=x + 5$ 12. $x=sqrt{2x + 11}+2$ column 2 red: $-20 = 4sqrt3{11x - 15}$ orange: $sqrt4{3x - 26}-1 = 1$ yellow: $7(4x + 17)^{\frac{1}{2}}-6 = 29$ light green: $45=-5sqrt{39 - 6x}$ dark green: $\frac{sqrt4{11x + 4}+17}{2}=10$ light blue: $10 = 18-4(29 - 7x)^{\frac{1}{3}}$ dark blue: $sqrt{2x + 39}=sqrt{9 - 4x}$ light purple: $sqrt4{83x - 18}=3sqrt4{x}$ dark purple: $(7x - 23)^{\frac{1}{3}}=(2x + 17)^{\frac{1}{3}}$ black: $sqrt{7x + 60}=x$ gray: $x - 3=sqrt{11x + 47}$ pink: $sqrt{24x + 25}-x = 7$ gina wilson (all things algebra), 2016

Explanation:

Let's solve problem 1 from Column 1: \(\boldsymbol{\sqrt{3x - 17}+2 = 7}\)

Step 1: Isolate the radical term

Subtract 2 from both sides of the equation to get the square root term by itself.
\(\sqrt{3x - 17}+2 - 2=7 - 2\)
\(\sqrt{3x - 17}=5\)

Step 2: Eliminate the square root

Square both sides of the equation to eliminate the square root. Remember that \((\sqrt{a})^2=a\) for \(a\geq0\).
\((\sqrt{3x - 17})^2 = 5^2\)
\(3x-17 = 25\)

Step 3: Solve for \(x\)

Add 17 to both sides of the equation.
\(3x-17 + 17=25 + 17\)
\(3x=42\)
Then divide both sides by 3.
\(\frac{3x}{3}=\frac{42}{3}\)
\(x = 14\)

Step 4: Check the solution (optional but recommended)

Substitute \(x = 14\) back into the original equation:
Left - hand side: \(\sqrt{3(14)-17}+2=\sqrt{42 - 17}+2=\sqrt{25}+2 = 5 + 2=7\)
Right - hand side: \(7\)
Since the left - hand side equals the right - hand side, \(x = 14\) is a valid solution.

Answer:

\(x = 14\)