Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 8) - √(x - 4) = 2

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 3) + √(x - 2) = 2

Solve each radical equation in Exercises 11–30. Check all proposed solutions. $\sqrt{1+4\sqrt{x}}=1+\sqrt{x}$

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^3/2 = 27

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^2/3 = 16

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. $(x^2-x-4{)}^{\frac{3}{4}}-2=6$

Solve each equation in Exercises 41–60 by making an appropriate substitution. $9x^4=25x^2-16$

Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. $x^{\frac{2}{5}}+x^{\frac{1}{5}}-6=0$

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)² - 4(x - 5) - 21 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. ${(y-\frac{8}{y})}^2+5(y-\frac{8}{y})-14=0$

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x - 2| = 7

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|3x - 2| = 14

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|4 - (5/2)x| + 6 = 18

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |4x - 3| = |4x - 5|

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. $\mid x^2-6\mid =\mid 5x\mid$

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. $\mid 2x^2-4\mid =\mid 2x^2\mid$

In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).]

a)b)c)d)e)f)

$y = \sqrt{x - 4} + \sqrt{x + 4} - 4$

In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).]

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$y = x^{-2} - x^{-1} - 6$

In Exercises 91–100, find all values of x satisfying the given conditions. y = |2 - 3x| and y = 13

In Exercises 91–100, find all values of x satisfying the given conditions. $y = x - \sqrt{x - 2} \quad \text{and} \quad y = 4$

In Exercises 91–100, find all values of x satisfying the given conditions. $y=x^3+4x^2-x+6$ and $y=10$

In Exercises 91–100, find all values of x satisfying the given conditions. $y = (x - 5)^{\frac{3}{2}} \quad \text{and} \quad y = 125$

In Exercises 91–100, find all values of x satisfying the given conditions.$y_1 = 6 \left( \frac{2x}{x - 3} \right)^2, \quad y_2 = 5 \left( \frac{2x}{x - 3} \right), \quad \text{and} \quad y_1 \text{ exceeds } y_2 \text{ by } 6.$