Question

directions: solve each proportion.

1. $\frac{9}{16}=\frac{x}{12}$
2. $\frac{x-3}{18}=\frac{12}{9}$
3. $\frac{7}{11}=\frac{18}{x+1}$
4. $\frac{3x-4}{14}=\frac{9}{10}$
5. $\frac{17}{15}=\frac{10}{2x-2}$
6. $\frac{x-16}{x+6}=\frac{3}{5}$
7. $\frac{6}{19}=\frac{x-12}{2x-2}$
8. $\frac{x-9}{15}=\frac{2x-9}{10}$
9. $\frac{x-9}{3}=\frac{56}{x+4}$
10. $\frac{7}{x+1}=\frac{2x-1}{36}$

© gina wilson (all things algebra®, llc), 2014-2018

Explanation:

Problem 13

Step1: Cross-multiply to eliminate fractions

$9 \times 12 = 16x$

Step2: Calculate left side, solve for x

$108 = 16x \implies x = \frac{108}{16} = \frac{27}{4}$

Problem 14

Step1: Cross-multiply to eliminate fractions

$9(x-3) = 12 \times 18$

Step2: Simplify both sides

$9x - 27 = 216$

Step3: Isolate x term

$9x = 216 + 27 = 243$

Step4: Solve for x

$x = \frac{243}{9} = 27$

Problem 15

Step1: Cross-multiply to eliminate fractions

$7(x+1) = 11 \times 18$

Step2: Simplify both sides

$7x + 7 = 198$

Step3: Isolate x term

$7x = 198 - 7 = 191$

Step4: Solve for x

$x = \frac{191}{7}$

Problem 16

Step1: Cross-multiply to eliminate fractions

$10(3x-4) = 9 \times 14$

Step2: Simplify both sides

$30x - 40 = 126$

Step3: Isolate x term

$30x = 126 + 40 = 166$

Step4: Solve for x

$x = \frac{166}{30} = \frac{83}{15}$

Problem 17

Step1: Cross-multiply to eliminate fractions

$17(2x-2) = 15 \times 10$

Step2: Simplify both sides

$34x - 34 = 150$

Step3: Isolate x term

$34x = 150 + 34 = 184$

Step4: Solve for x

$x = \frac{184}{34} = \frac{92}{17}$

Problem 18

Step1: Cross-multiply to eliminate fractions

$5(x-16) = 3(x+6)$

Step2: Expand both sides

$5x - 80 = 3x + 18$

Step3: Isolate x terms

$5x - 3x = 18 + 80$

Step4: Solve for x

$2x = 98 \implies x = 49$

Problem 19

Step1: Cross-multiply to eliminate fractions

$6(2x-2) = 19(x-12)$

Step2: Expand both sides

$12x - 12 = 19x - 228$

Step3: Isolate x terms

$-12 + 228 = 19x - 12x$

Step4: Solve for x

$216 = 7x \implies x = \frac{216}{7}$

Problem 20

Step1: Cross-multiply to eliminate fractions

$10(x-9) = 15(2x-9)$

Step2: Expand both sides

$10x - 90 = 30x - 135$

Step3: Isolate x terms

$-90 + 135 = 30x - 10x$

Step4: Solve for x

$45 = 20x \implies x = \frac{45}{20} = \frac{9}{4}$

Problem 21

Step1: Cross-multiply to eliminate fractions

$(x-9)(x+4) = 3 \times 56$

Step2: Expand and simplify

$x^2 -5x -36 = 168$

Step3: Rearrange to quadratic form

$x^2 -5x -204 = 0$

Step4: Factor quadratic

$(x-17)(x+12) = 0$

Step5: Solve for x

$x = 17$ or $x = -12$

Problem 22

Step1: Cross-multiply to eliminate fractions

$7 \times 36 = (2x-1)(x+1)$

Step2: Expand and simplify

$252 = 2x^2 + x -1$

Step3: Rearrange to quadratic form

$2x^2 + x -253 = 0$

Step4: Factor quadratic

$(2x+23)(x-11) = 0$

Step5: Solve for x

$x = 11$ or $x = -\frac{23}{2}$

Answer:

1. $\boldsymbol{x=\frac{27}{4}}$
2. $\boldsymbol{x=27}$
3. $\boldsymbol{x=\frac{191}{7}}$
4. $\boldsymbol{x=\frac{83}{15}}$
5. $\boldsymbol{x=\frac{92}{17}}$
6. $\boldsymbol{x=49}$
7. $\boldsymbol{x=\frac{216}{7}}$
8. $\boldsymbol{x=\frac{9}{4}}$
9. $\boldsymbol{x=17}$ or $\boldsymbol{x=-12}$
10. $\boldsymbol{x=11}$ or $\boldsymbol{x=-\frac{23}{2}}$