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1) \\(\\frac{x - 9}{10} = \\frac{7}{4}\\)\ 2) \\(\\frac{9}{r - 10} = \\…

Question

  1. \\(\frac{x - 9}{10} = \frac{7}{4}\\)\
  2. \\(\frac{9}{r - 10} = \frac{4}{6}\\)\
  3. \\(\frac{10}{9} = \frac{m + 8}{5}\\)\
  4. \\(\frac{10}{k - 5} = \frac{7}{9}\\)\
  5. \\(\frac{4}{8} = \frac{7}{k - 5}\\)\
  6. \\(\frac{7}{3} = \frac{p + 10}{8}\\)\
  7. \\(\frac{4}{10} = \frac{8}{r + 1}\\)\
  8. \\(\frac{a - 8}{6} = \frac{7}{5}\\)\
  9. \\(\frac{8}{b - 2} = \frac{4}{3}\\)\
  10. \\(\frac{x + 5}{3} = \frac{9}{6}\\)\
  11. \\(\frac{5}{m - 3} = \frac{6}{m - 5}\\)\
  12. \\(\frac{p + 10}{p + 7} = \frac{4}{9}\\)\
  13. \\(\frac{6}{5} = \frac{a - 9}{a + 2}\\)\
  14. \\(\frac{5}{v + 7} = \frac{7}{v - 2}\\)\
  15. \\(\frac{m - 4}{m + 8} = \frac{2}{9}\\)\
  16. \\(\frac{x - 10}{9} = \frac{x - 6}{4}\\)\
  17. \\(\frac{k + 4}{6} = \frac{k + 1}{7}\\)\
  18. \\(\frac{v - 8}{v - 7} = \frac{4}{10}\\)\
  19. \\(\frac{6}{n - 5} = \frac{5}{n + 9}\\)\
  20. \\(\frac{8}{r - 9} = \frac{10}{r + 6}\\)

Explanation:

1) Step1: Cross-multiply to eliminate fractions

$4(x-9)=7\times10$

1) Step2: Simplify both sides

$4x-36=70$

1) Step3: Isolate $4x$

$4x=70+36$
$4x=106$

1) Step4: Solve for $x$

$x=\frac{106}{4}=\frac{53}{2}$

---

2) Step1: Cross-multiply to eliminate fractions

$9\times6=4(r-10)$

2) Step2: Simplify both sides

$54=4r-40$

2) Step3: Isolate $4r$

$4r=54+40$
$4r=94$

2) Step4: Solve for $r$

$r=\frac{94}{4}=\frac{47}{2}$

---

3) Step1: Cross-multiply to eliminate fractions

$10\times5=9(m+8)$

3) Step2: Simplify both sides

$50=9m+72$

3) Step3: Isolate $9m$

$9m=50-72$
$9m=-22$

3) Step4: Solve for $m$

$m=-\frac{22}{9}$

---

4) Step1: Cross-multiply to eliminate fractions

$10\times9=7(k-5)$

4) Step2: Simplify both sides

$90=7k-35$

4) Step3: Isolate $7k$

$7k=90+35$
$7k=125$

4) Step4: Solve for $k$

$k=\frac{125}{7}$

---

5) Step1: Cross-multiply to eliminate fractions

$4(k-5)=7\times8$

5) Step2: Simplify both sides

$4k-20=56$

5) Step3: Isolate $4k$

$4k=56+20$
$4k=76$

5) Step4: Solve for $k$

$k=19$

---

6) Step1: Cross-multiply to eliminate fractions

$7\times8=3(p+10)$

6) Step2: Simplify both sides

$56=3p+30$

6) Step3: Isolate $3p$

$3p=56-30$
$3p=26$

6) Step4: Solve for $p$

$p=\frac{26}{3}$

---

7) Step1: Cross-multiply to eliminate fractions

$4(r+1)=8\times10$

7) Step2: Simplify both sides

$4r+4=80$

7) Step3: Isolate $4r$

$4r=80-4$
$4r=76$

7) Step4: Solve for $r$

$r=19$

---

8) Step1: Cross-multiply to eliminate fractions

$5(a-8)=7\times6$

8) Step2: Simplify both sides

$5a-40=42$

8) Step3: Isolate $5a$

$5a=42+40$
$5a=82$

8) Step4: Solve for $a$

$a=\frac{82}{5}$

---

9) Step1: Cross-multiply to eliminate fractions

$8\times3=4(b-2)$

9) Step2: Simplify both sides

$24=4b-8$

9) Step3: Isolate $4b$

$4b=24+8$
$4b=32$

9) Step4: Solve for $b$

$b=8$

---

10) Step1: Cross-multiply to eliminate fractions

$6(x+5)=9\times3$

10) Step2: Simplify both sides

$6x+30=27$

10) Step3: Isolate $6x$

$6x=27-30$
$6x=-3$

10) Step4: Solve for $x$

$x=-\frac{1}{2}$

---

11) Step1: Cross-multiply to eliminate fractions

$5(m-5)=6(m-3)$

11) Step2: Expand both sides

$5m-25=6m-18$

11) Step3: Isolate $m$

$6m-5m=-25+18$
$m=-7$

---

12) Step1: Cross-multiply to eliminate fractions

$9(p+10)=4(p+7)$

12) Step2: Expand both sides

$9p+90=4p+28$

12) Step3: Isolate $5p$

$9p-4p=28-90$
$5p=-62$

12) Step4: Solve for $p$

$p=-\frac{62}{5}$

---

13) Step1: Cross-multiply to eliminate fractions

$6(a+2)=5(a-9)$

13) Step2: Expand both sides

$6a+12=5a-45$

13) Step3: Isolate $a$

$6a-5a=-45-12$
$a=-57$

---

14) Step1: Cross-multiply to eliminate fractions

$5(v-2)=7(v+7)$

14) Step2: Expand both sides

$5v-10=7v+49$

14) Step3: Isolate $-2v$

$7v-5v=-10-49$
$2v=-59$

14) Step4: Solve for $v$

$v=-\frac{59}{2}$

---

15) Step1: Cross-multiply to eliminate fractions

$9(m-4)=2(m+8)$

15) Step2: Expand both sides

$9m-36=2m+16$

15) Step3: Isolate $7m$

$9m-2m=16+36$
$7m=52$

15) Step4: Solve for $m$

$m=\frac{52}{7}$

---

16) Step1: Cross-multiply to eliminate fractions

$4(x-10)=9(x-6)$

16) Step2: Expand both sides

$4x-40=9x-54$

16) Step3: Isolate $-5x$

$9x-4x=-40+54$
$5x=14$

16) Step4: Solve for $x$

$x=\frac{14}{5}$

---

17) Step1: Cross-multiply to eliminate fractions

$7(k+4)=6(k+1)$

17) Step2: Expand both sides

$7k+28=6k+6$

17) Step3: Isolate $k$

$7k-6k=6-28$
$k=-22$

---

18) Step1: Cross-multiply to eliminate fractions

$10(v-8)=4(v-7)$

18) Step2: Expand both sides

$10v-80=4v-28$

18) Step3: Isolate $6v$

$10v-4v=-28+80$
$…

Answer:

  1. $x=\frac{53}{2}$
  2. $r=\frac{47}{2}$
  3. $m=-\frac{22}{9}$
  4. $k=\frac{125}{7}$
  5. $k=19$
  6. $p=\frac{26}{3}$
  7. $r=19$
  8. $a=\frac{82}{5}$
  9. $b=8$
  10. $x=-\frac{1}{2}$
  11. $m=-7$
  12. $p=-\frac{62}{5}$
  13. $a=-57$
  14. $v=-\frac{59}{2}$
  15. $m=\frac{52}{7}$
  16. $x=\frac{14}{5}$
  17. $k=-22$
  18. $v=\frac{26}{3}$
  19. $n=-79$
  20. $r=69$