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. $5\sqrt3{2x + 11}=15$
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. $\sqrt{13x + 27}=4\sqrt{x}$
10. $x = \sqrt{10x - 24}$
11. $\sqrt{7x + 43}=x + 5$
12. $x = \sqrt{2x + 11}+2$

column 2
red: $-20 = 4\sqrt3{11x - 15}$
orange: $\sqrt4{3x - 26}-1 = 1$
yellow: $7(4x + 17)^{\frac{1}{2}}-6 = 29$
light green: $45 = -5\sqrt{39 - 6x}$
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: $\sqrt4{83x - 18}=3\sqrt4{x}$
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 5 from Column 1: \( 3 = 11 - (4 - 6x)^{\frac{1}{2}} \)

Step 1: Isolate the radical term

Subtract 11 from both sides:
\( 3 - 11 = - (4 - 6x)^{\frac{1}{2}} \)
\( -8 = - (4 - 6x)^{\frac{1}{2}} \)

Step 2: Simplify the equation

Multiply both sides by -1:
\( 8 = (4 - 6x)^{\frac{1}{2}} \)
Since \( (4 - 6x)^{\frac{1}{2}} = \sqrt{4 - 6x} \), we have:
\( \sqrt{4 - 6x} = 8 \)

Step 3: Eliminate the square root

Square both sides:
\( (\sqrt{4 - 6x})^2 = 8^2 \)
\( 4 - 6x = 64 \)

Step 4: Solve for \( x \)

Subtract 4 from both sides:
\( -6x = 64 - 4 \)
\( -6x = 60 \)
Divide both sides by -6:
\( x = \frac{60}{-6} \)
\( x = -10 \)

Answer:

\( x = -10 \)