Solve the following inequality:
\$ - 9 < 2(5 - 3x) + 4( 3 + x) le 2 \$

A) \$ 10 le x < 31/2 \$

B) \$ 10 ge x > 31/2 \$

C) \$ 7 le x < 11/3\$

D) \$ 10 ge x < 31/2 \$

Solve the nonlinear equation:
\$sqrt(x+1) + root(3){x+1} = 2 \$

A) 1

B) 0

C) 2

D) \$\sqrt3\$

Determine the number of solutions for the following system of linear equations:
3x - 2y = 6 6x - 4y = 12

A) Unique solutions

B) No solutions

C) Not enough information

D) Infinitely many solutions

If there is no solution to the linear equation system 4x - ky = 13, 7x + 6y = 9, then find the value of k.

A) \$ k = 7/24 \$

B) \$ k = - 3/7 \$

C) \$ k = - 24/7 \$

D) \$ k = - 11/2 \$

Solve the following equation for x:
2(3x - 4) + \$1/2\$ (5x + 3) = 4 - \$2/3\$ (2x + 1)

A) 2

B) 1

C) 0

D) 1.1

Solve the following system of equations:
2s - 3d = 11 5s + 4d = 2

A) s = \$50/25\$, d = - \$51/25\$

B) s = \$51/23\$, d = - \$50/23\$

C) s = \$50/23\$, d = - \$51/23\$

D) s = \$51/25\$, d = - \$50/25\$

Simplify the expression and find an equivalent expression:
\$ (3x^2 - 9xy + 6y^2)/(x^2 - 4xy + 4y^2) \$

A) \$ (3(x + y))/(3x + 2y) \$

B) \$ (3(x - 4y))/(x + 2y) \$

C) \$ (x - y)/(x - 2y) \$

D) \$ (3(x - y))/(x - 2y) \$

The linear function f(x) = 3x − 5 is graphed on the coordinate plane. If the point (a,b) lies on the graph of f(x), and f(a) = 7, find the value of b.

A) b = 4

B) b = 6

C) b = 7

D) b = 5

Write an equation for a line perpendicular to f(x) = 3x − 8 and passing through the point (5, 13).

A) \$ y = 1/3 x + 22/3 \$

B) \$ y = - 2/3 x - 13/3 \$

C) \$ y = - 1/3 x + 44/3 \$

D) \$ y = 3/8 x + 11/8 \$

If the linear system ax + by = 7 and cx + dy = 5 has no solution, find the relationship between a,b,c, and d.

A) ad - bc = 35

B) ad - bc = - 35

C) ac + bd = 35

D) ab - dc = 35