Question

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1. solve for x and simplify the answer fully.

$\frac{2x + 7}{5} = \frac{3x - 6}{6}$

1. solve for x and simplify the answer fully.

$\frac{x - 8}{7} = \frac{x + 4}{3}$

1. solve for x and simplify the answer fully.

$\frac{2}{x + 5} = \frac{3}{5x + 4}$

1. solve for x and simplify the answer fully.

$\frac{x + 5}{x - 5} = \frac{5}{6}$

1. solve for x and simplify the answer fully.

$\frac{x + 9}{2} = \frac{x + 1}{3}$

Explanation:

Problem 11

Step1: Cross-multiply to eliminate denominators

$6(2x + 7) = 5(3x - 6)$

Step2: Expand both sides

$12x + 42 = 15x - 30$

Step3: Rearrange terms to isolate x

$42 + 30 = 15x - 12x$

Step4: Simplify and solve for x

$72 = 3x \implies x = \frac{72}{3} = 24$

Problem 12

Step1: Cross-multiply to eliminate denominators

$3(x - 8) = 7(x + 4)$

Step2: Expand both sides

$3x - 24 = 7x + 28$

Step3: Rearrange terms to isolate x

$-24 - 28 = 7x - 3x$

Step4: Simplify and solve for x

$-52 = 4x \implies x = \frac{-52}{4} = -13$

Problem 13

Step1: Cross-multiply to eliminate denominators

$2(5x + 4) = 3(x + 5)$

Step2: Expand both sides

$10x + 8 = 3x + 15$

Step3: Rearrange terms to isolate x

$10x - 3x = 15 - 8$

Step4: Simplify and solve for x

$7x = 7 \implies x = \frac{7}{7} = 1$

Problem 14

Step1: Cross-multiply to eliminate denominators

$6(x + 5) = 5(x - 5)$

Step2: Expand both sides

$6x + 30 = 5x - 25$

Step3: Rearrange terms to isolate x

$6x - 5x = -25 - 30$

Step4: Simplify and solve for x

$x = -55$

Problem 15

Step1: Cross-multiply to eliminate denominators

$3(x + 9) = 2(x + 1)$

Step2: Expand both sides

$3x + 27 = 2x + 2$

Step3: Rearrange terms to isolate x

$3x - 2x = 2 - 27$

Step4: Simplify and solve for x

$x = -25$

Answer:

1. $x = 24$
2. $x = -13$
3. $x = 1$
4. $x = -55$
5. $x = -25$