Answer:

\(6x^2-\left(2x+3\right)\left(3x-2\right)=7\)

\(\Rightarrow6x^2-\left(6x^2+9x-4x-6\right)=7\)

\(\Rightarrow6x^2-\left(6x^2+5x-6\right)=7\)

\(\Rightarrow6x^2-6x^2-5x+6=7\)

\(\Rightarrow-5x+6=7\)

\(\Rightarrow-5x=1\)

\(\Rightarrow x=\frac{-1}{5}\)

\(5x\left(12+7\right)-3x\left(80x-5\right)=-100\)

\(\Rightarrow5x.19-240x^2+15x=-100\)

\(\Rightarrow95x-240x^2+15x=-100\)

\(\Rightarrow-240x^2+110x+100=0\)

\(\Rightarrow-24x^2-11x-10=0\)

\(\Rightarrow24\left(x^2-\frac{11}{24}x+\frac{121}{2304}\right)-\frac{1081}{96}=0\)

\(\Rightarrow24\left(x-\frac{11}{48}\right)^2-\frac{1081}{96}=0\)

\(\Rightarrow24\left(x-\frac{11}{48}\right)^2=\frac{1081}{2304}\)

\(\Rightarrow\left(x-\frac{11}{48}\right)^2=\left(\frac{\pm\sqrt{1081}}{48}\right)^2\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{11}{48}=\frac{\sqrt{1081}}{48}\\x-\frac{11}{48}=\frac{-\sqrt{1081}}{48}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{\sqrt{1081}+11}{48}\\x=\frac{11-\sqrt{1081}}{48}\end{cases}}\)

\(\left(3x-5\right)\left(7-5x\right)-\left(5x-2\right)\left(2-3x\right)=4\)

\(\Rightarrow\left(21x-15x^2-35+25x\right)-\left(10x-15x^2-4+6x\right)-4=0\)

\(\Rightarrow36x-15x^2-35-16x+15x^2+4-4=0\)

\(\Rightarrow\left(-15x^2+15x^2\right)+\left(36x-16x\right)+\left(-35+4-4\right)=0\)

\(\Rightarrow30x-35=0\)

\(\Rightarrow x=\frac{7}{6}\)

a)100-7.[x-5]=58

          7.[x-5]=100-58=42

               x-5=42:7=6

                  x=6+5

                  x=11

b)12.[x-1]:3=4³+2³

   12 [x-1]:3=64+8

   12.[x-1]:3=72

        [x-1]:3=72:12=6

           [x-1]=6.3=18

                x=18-1

                x=17

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a, \(-4x+5+2x-1=3\Leftrightarrow-2x=-1\Leftrightarrow x=\dfrac{1}{2}\)

b, \(-2x+2=2\Leftrightarrow x=0\)

c, \(-2x-6=-8\Leftrightarrow x=1\)

a)

<=> 10x - 35 + 16x - 10 = 5 

<=> 10x + 16x = 5 + 35 + 10

<=> 26x = 50

<=> x = 50/26 = 25/13

a) 5^x-1 = 5^2 + 100

=> 5^x-1 = 125 = 5³

=> x - 1 = 3

=> x = 4.

b) x¹⁰ = x

=> x = {-1;0;1}

2.5².3² + {[2.5³ - (5x + 4).5 : (2³.3.5)]} = 455

=> 450 + {250 - (5x + 4).5 : 120} = 455

=> 250 - (5x + 4).5 : 120 = 5

=> (5x + 4).5 : 120 = 245

=> (5x + 4).5 = 245.120 = 29400

=> 5x + 4 = 29400 : 5 = 5880

=> 5x = 5876

=> x = 1175,2

1) (x - 35) - 120 = 0

x - 35 = 120

x = 120 + 35

x = 155

2) 310 - (118 - x) = 217

118 - x = 310 - 217

118 - x = 93

x = 118 - 93

x = 25

3) 156 - (x + 61) = 82

x + 61 = 156 - 82

x + 61 = 74

x = 74 - 61

x = 13

4) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305 = 407

5) 100 - 7 - (x - 5) = 58

x - 5 = 93 - 58

x - 5 = 35

x = 35 + 5 = 40

6) 12(x - 1) : 3 = 4³ + 2³

4(x - 1) = 72

x - 1 = 18

x = 18 + 1 = 19

7) 24 + 5x = 7⁵ : 7³

24 + 5x = 49

5x = 25

x = 25 : 5 = 5

8) 5(x - 1) : 3 = 4³ + 2³

\(\dfrac{5}{3}\left(x-1\right)=72\)

x - 1 = \(\dfrac{216}{5}\)

x = 221/5

9) 5(x - 4)² - 7 = 13

5(x - 4)² = 20

(x - 4)² = 4

\(\Rightarrow\left[{}\begin{matrix}x-4=2\\x-4=-2\end{matrix}\right.\)   \(\Rightarrow\left[{}\begin{matrix}x=6\\x=2\end{matrix}\right.\)

10) (x + 1) + (x + 2) + ... + (x + 30) = 795

=> (x + x + x + ... + x) + (1 + 2 + 3 +...+ 30) = 795 (1)

Đặt A = 1 + 2 + 3 +...+ 30

Số số hạng trong A là: (30 - 1) : 1 + 1 = 30 (số)

Tổng A bằng : (30 + 1).30 : 2 =465

Thay A = 465 vào (1) , ta được:

30x + 465 = 795

=> 30x =330

=> x =11

1: =>x-35=120

=>x=120+35=155

2: =>118-x=310-217=93

=>x=118-93=25

3: =>x+61=156-82=74

=>x=74-61=13

4: =>x-305=814-712=102

=>x=102+305=407

5: =>93-(x-5)=58

=>x-5=35

=>x=40

6: =>4(x-1)=64+8=72

=>x-1=18

=>x=19

7: =>5x+24=49

=>5x=25

=>x=5

8: =>5(x-1):3=4^3+2^3=64+8=72

=>5(x-1)=216

=>x-1=216/5

=>x=221/5

`Answer:`

\(3\left(\frac{5}{3}x-7\right)-2\left(1.5x+6\right)-\left(5-x\right)\left(x+4\right)=80+x^2\)

\(\Leftrightarrow3\left(\frac{5x}{3}-7\right)-2\left(5x+6\right)-\left(5-x\right)\left(x+4\right)=80+x^2\)

\(\Leftrightarrow5x-21-10x-12-5x-20+x^2+4x=80+x^2\)

\(\Leftrightarrow5x-21-10x-12-5x-20+4x=80\)

\(\Leftrightarrow-6x-53=80\)

\(\Leftrightarrow-6x=133\)

\(\Leftrightarrow x=-\frac{133}{6}\)

\(\frac{4}{5}x^2\left(\frac{x}{3}-\frac{1}{2}\right)-\left(\frac{1}{5}x-\frac{2}{3}\right)\left(4\frac{x^2}{3}+1\right)=\frac{22}{45}x^2\)

\(\Leftrightarrow36x^2\left(\frac{x}{3}-\frac{1}{2}\right)-45\left(\frac{x}{5}-\frac{2}{3}\right)\left(\frac{4x^2}{3}+1\right)=22x^2\)

\(\Leftrightarrow12x^3-18x^2-12x^3-9x+40x^2+30=22x^2\)

\(\Leftrightarrow22x^2-9x+30=22x^2\)

\(\Leftrightarrow-9x+30=0\)

\(\Leftrightarrow-9x=-30\)

\(\Leftrightarrow x=\frac{10}{3}\)