Lời giải:

a)

\(|x|=2019\Rightarrow \left[\begin{matrix} x=2019\\ x=-2019\end{matrix}\right.\)

b)

\(|x-3|=21\Rightarrow \left[\begin{matrix} x-3=21\\ x-3=-21\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=24\\ x=-18\end{matrix}\right.\)

c)

\(|x|-25+x=9\)

\(\Leftrightarrow |x|+x=34\)

Nếu $x\geq 0$: $|x|=x$

\(\Rightarrow x+x=34\Rightarrow 2x=34\Rightarrow x=17\) (thỏa mãn)

Nếu $x< 0$: $|x|=-x$

$\Rightarrow -x+x=34\Rightarrow 0=34$ (vô lý -loại)

Vậy $x=17$

d) \(|x-2|+2x=4\)

Nếu $x\geq 2\Rightarrow |x-2|=x-2$

$\Rightarrow x-2+2x=4\Rightarrow 3x=6\Rightarrow x=2$ (thỏa mãn)

Nếu $x< 2\Rightarrow |x-2|=2-x$

$\Rightarrow 2-x+2x=4\Rightarrow x=2$ (loại vì $x< 2$)

Vậy $x=2$

e)

$|x-5|+3x+2=13$

Nếu $x\geq 5$ thì $|x-5|=x-5$

\(\Rightarrow x-5+3x+2=13\)

\(\Leftrightarrow 4x=16\Leftrightarrow x=4\) (loại vì $x\geq 5$)

Nếu $x< 5$ thì $|x-5|=5-x$

$\Rightarrow 5-x+3x+2=13$

$\Leftrightarrow 2x=6\Rightarrow x=3$ (thỏa mãn)

Vậy $x=3$

\(a,2\frac{x}{7}=\frac{75}{35}\)

\(\frac{75}{35}=2\frac{5}{35}=2\frac{1}{7}\)

\(\Rightarrow x=1\)

\(b,47:4=...\left(+3\right)\)

     \(\Rightarrow\left(47-3\right):4=11\)

      \(\Rightarrow x=11\)

\(c,\frac{112}{5}=\frac{336}{15}=22\left(+6\right)\)

     \(\Rightarrow x=22\frac{x=6}{15}\)

\(d,7,5x=\frac{75x}{100}:\left(9-6\frac{13}{21}\right)=2\frac{13}{25}\)

     \(\frac{75x}{100}:\left(9-\frac{139}{21}\right)=\frac{63}{25}\)

       \(\frac{75x}{100}:\frac{50}{21}=\frac{63}{25}\)

           \(\Rightarrow\frac{63^3}{25^{\left(1\right)}}\cdot\frac{50^{\left(2\right)}}{21^1}=6=\frac{6}{1}\)

             \(\Rightarrow\frac{6}{1}=\frac{600}{100}\)

Con d sai đề

\(a,70-5\times\left(x-3\right)=45\)

\(5\times\left(x-3\right)=70-45\)

\(5\times\left(x-3\right)=25\)

\(x-3=25:5\)

x - 3 = 5

x = 5 + 3 = 8

vậy x = 8

\(b,12+\left(5+x\right)=20\)

12 + 5 + x = 20

17 + x = 20

x = 20 - 17 = 3

vậy x = 3

c, 130 - (100 + x) = 25

130 - 100 - x = 25

30 - x = 25

x = 30 - 25 = 5

vậy x = 5

\(g,10+2\times x=4^5:4^3\)

\(10+2\times x=4^2\)

\(10+2\times x=16\)

\(2\times x=16-10\)

\(2\times x=6\)

x = 6 : 2 = 3

vậy x = 3

h, \(14\times x+54=82\)

\(14\times x=82-54\)

\(14\times x=28\)

\(x=28:14=2\)

vậy x = 2

\(k,15\times x-133=17\)

\(15\times x=17+133\)

\(15\times x=150\)

\(x=150:15=10\)

vậy x = 10

\(a,70-5\times\left(x-3\right)=45\)

\(5\times\left(x-3\right)=70-45\)

\(5\times\left(x-3\right)=25\)

\(x-3=25:5\)

x - 3 = 5

x = 5 + 3 = 8

vậy x = 8

\(b,12+\left(5+x\right)=20\)

12 + 5 + x = 20

17 + x = 20

x = 20 - 17 = 3

vậy x = 3

c, 130 - (100 + x) = 25

130 - 100 - x = 25

30 - x = 25

x = 30 - 25 = 5

vậy x = 5

\(g,10+2\times x=4^5:4^3\)

\(10+2\times x=4^2\)

\(10+2\times x=16\)

\(2\times x=16-10\)

\(2\times x=6\)

x = 6 : 2 = 3

vậy x = 3

h, \(14\times x+54=82\)

\(14\times x=82-54\)

\(14\times x=28\)

\(x=28:14=2\)

vậy x = 2

\(k,15\times x-133=17\)

\(15\times x=17+133\)

\(15\times x=150\)

\(x=150:15=10\)

vậy x = 10

a/ => (x² - 5)(x + 5)(x - 5) = 0 

=> x² - 5 = 0 => x² = 5 => x = \(+-\sqrt{5}\) (loại)

hoặc x + 5 = 0 => x = -5

hoặc x - 5 = 0 => x = 5

Vậy x = 5 ; x = -5

b/ => x + 5 = 0 => x = -5

hoặc 9 + x² = 0 => x² = -9 (vô nghiệm)

Vậy x = -5

c/ => x + 3 = 0 => x = -3

hoặc x² + 1 = 0 => x² = -1 (vô nghiệm)

Vậy x = -3

d/ => (x + 5)(x + 2)(x - 2) = 0 

=> x + 5 = 0 => x = -5

hoặc x + 2 = 0 => x = -2

hoặc x - 2 = 0 => x = 2

Vậy x = -5 ; x = -2; x = 2

a) \(\left(x^2-5\right)\left(x^2-25\right)< 0\)

Vì \(x^2-5>x^2-25\) nên \(\left\{{}\begin{matrix}x^2-5>0\\x^2-25< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2>5\\x^2< 25\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{5}< x< -\sqrt{5}\left(vl\right)\\-5< x< 5\end{matrix}\right.\)

b) \(\left(x+5\right)\left(9+x^2\right)< 0\)

Vì \(9+x^2>0\) nên \(x+5< 0\Leftrightarrow x< -5\)

c) \(\left(x+3\right)\left(x^2+1\right)=0\)

Vì \(x^2+1>0\) nên \(x+3=0\Leftrightarrow x=-3\)

d) \(\left(x+5\right)\left(x^2-4\right)=0\)

\(\Rightarrow\left(x+5\right)\left(x+2\right)\left(x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=-2\\x=2\end{matrix}\right.\)

a, <=>(-5)^x=(-5)³

<=> x=3

b, <=> 5^2x=5²²

<=> x=11

c, 3^2x=3¹⁷.3¹⁵

<=> 3^2x=3³²

<=> x=16

d,2^x+1=2²⁵

<=> x+1=25

<=> x=24

Chúc hok tốt!!!

a)x=3

b)x=11

c)x=16

d)x=24

a,|x|+3=5

\(\Leftrightarrow\left|x\right|=5-3=2\)

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

b,|x+3|=5

\(\Rightarrow\left\{{}\begin{matrix}x+3=5\\x+3=-5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2\\-8\end{matrix}\right.\)

c,|x-7|+13=25

<=>|x-7|=25-13=12

\(\Rightarrow\left\{{}\begin{matrix}x-7=12\\x-7=-12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=19\\x=-5\end{matrix}\right.\)

d,\(26-\left|x+9\right|=-13\)

\(\Leftrightarrow\left|x+9\right|=26-\left(-13\right)=39\)

\(\Rightarrow\left\{{}\begin{matrix}x+9=39\\x+9=-39\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=30\\x=-48\end{matrix}\right.\)

e,8-|x|=15

<=>|x|=8-15=-7

\(\Rightarrow\left\{{}\begin{matrix}x=-7\\x=7\end{matrix}\right.\)

f,6-|-3+x|=-15

\(\Leftrightarrow\left|-3+x\right|=6-\left(-15\right)=21\)

\(\Rightarrow\left\{{}\begin{matrix}-3+x=21\\-3+x=-21\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=24\\x=-18\end{matrix}\right.\)

a, |x| + 3 = 5

|x| = 5 - 3

|x| = 2

|x| = 2 hoặc |x| = -2

Vậy |x| thuộc {2; -2}

b,|x + 3| = 5

|x + 3| = 5 hoặc |x + 3| = -5

x = 5 - 3 x = (-5) - 3

x = 2 x = -8

Vậy x thuộc {2; -8}

c,|x - 7| + 13 = 25

|x - 7| = 25 - 13

|x - 7| = 12

|x - 7| = 12 hoặc |x - 7| = -12

x = 12 + 7 x = (-12) + 7

x = 19 x = -5

Vậy x thuộc {19 ; -5}