👤

Answer :

Answer:

(1) [tex]x=-14\frac{7}{9}[/tex]

(2) [tex]x=72[/tex]

(3) [tex]x=11[/tex]

(4) [tex]x=-1\frac{7}{11}[/tex]

(5) [tex]x=-36[/tex]

(6) [tex]x=-61[/tex]

(7) [tex]x=-12[/tex]

(8) [tex]x=1\frac{4}{5}[/tex]

(9) [tex]x=9[/tex]

(10) [tex]x=18[/tex]

Step-by-step explanation:

One thing that will be very useful in solving these problems is the distributive property, that states [tex]a(b-c)=ab-ac[/tex].

(1) Use the distributive property to open the parentheses, getting:

[tex]5x-14x+154=287[/tex]

Then, combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]-9x=133[/tex]

Divide both sides by -9 to get:

[tex]x=-14\frac{7}{9}[/tex]

(2) Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]-8x=-576[/tex]

Divide both sides by -8 to get:

[tex]x=72[/tex]

(3) Use the distributive property to open the parentheses, getting:

[tex]7x+14x-56=175[/tex]

Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]21x=231[/tex]

Divide both sides by 21 to get:

[tex]x=11[/tex]

(4) Use the distributive property to open the parentheses, getting:

[tex]123=4x-15x+105[/tex]

Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]-11x=18[/tex]

Divide both sides by -11 to get:

[tex]x=-1\frac{7}{11}[/tex]

(5) Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]-4x=144[/tex]

Divide both sides by -4 to get:

[tex]x=-36[/tex]

(6) Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]-8x=488[/tex]

Divide both sides by -8 to get:

[tex]x=-61[/tex]

(7) Use the distributive property to open the parentheses, getting:

[tex]240=2x-12x+120[/tex]

Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]-10x=120[/tex]

Divide both sides by -10 to get:

[tex]x=-12[/tex]

(8) Use the distributive property to open the parentheses, getting:

[tex]9=6x+9x-18[/tex]

Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]15x=27[/tex]

Divide both sides by 15 to get:

[tex]x=1\frac{4}{5}[/tex]

(9) Simplify the left side of the equation to get:

[tex]x-3=6[/tex]

Add 3 to both sides to arrive at:

[tex]x=9[/tex]

(10) Use the distributive property to open the parentheses, getting:

[tex]64=4x+2x-44[/tex]

Combine like terms and isolate [tex]x[/tex] on one side to get:

[tex]6x=108[/tex]

Divide both sides by 6 to get:

[tex]x=18[/tex]

Hope this helps :)

P.S. These problems took 1 hour for me to solve and type the solutions. Please give Brainliest if this answer helped you :)

Solution(s):

Question-1:

  • 5x - 7(2x - 22) = 287
  • => 5x - 14x + 154 = 287
  • => -9x + 154 = 287
  • => -9x = 287 - 154
  • => -9x = 133
  • => x = 133/-9 = -133/9

Question-2:

  • 20x + 136 = 28x - 440
  • => 440 + 136 = 28x - 20x
  • => 576 = 8x
  • => x = 576/8 = 72

Question-3:

  • 7x + 7(2x - 8) = 175
  • => 7x + 14x - 56 = 175
  • => 7x + 14x = 175 + 56
  • => 21x = 231
  • => x = 231/21 = 11

Question-4:

  • 123 = 4x - 5(3x - 21)
  • => 123 = 4x - 15x + 105
  • => 123 = -11x + 105
  • => 123 - 105 = -11x
  • => 18 = -11x
  • => x = -18/11

Question-5:

  • 23x - 87 = 57 + 27x
  • => -57 - 87 = 27x - 23x
  • => -144 = 4x
  • => x = -144/4 = -36

Question-6:

  • 22x - 164 = 30x + 324
  • => -324 - 164 = 30x - 22x
  • => -488 = 8x
  • => x = -488/8 = -61

Question-7:

  • 240 = 2x - 6(2x - 20)
  • => 240 = 2x - 12x + 120
  • => 240 = -10x + 120
  • => 120 = -10x
  • => x = -12

Question-8:

  • 9 = 6x + 3(3x - 6)
  • => 9 = 6x + 9x - 18
  • => 9 = 15x - 18
  • => 27 = 15x
  • => x = 27/15 = 9/5 = 1.8

Question-9:

  • {13x - 39}/13 = 6
  • => 13x/13 - 39/13 = 6
  • => x - 3 = 6
  • => x = 9

Question-10:

  • 64 = 4x + 2(x - 22)
  • => 64 = 4x + 2x - 44
  • => 64 = 6x - 44
  • => 108 = 6x
  • => x = 108/6 = 18

Hoped this helped!

Go Teaching: Other Questions