Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-13x+7=15+8x\)
2. \(-4x-12=11+x\)
3. \(12x+3=-12-11x\)
4. \(-14x-1=5+x\)
5. \(10x+9=6-3x\)
6. \(-11x+3=-10+x\)
7. \(-11x-8=12+x\)
8. \(-x-9=15+3x\)
9. \(9x-15=-2-13x\)
10. \(-8x+9=15+x\)
11. \(13x-6=-8+4x\)
12. \(-13x+9=-2+7x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+7}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-8x } & = & 15 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &-21x & = &8\\\Leftrightarrow & \color{red}{-21}x & = &8\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{8}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{21} } & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x } & = & 11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+3}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3+11x } & = & -12 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &23x & = &-15\\\Leftrightarrow & \color{red}{23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+9}& = & 6 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+3x } & = & 6 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & 12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-12x & = &20\\\Leftrightarrow & \color{red}{-12}x & = &20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-9}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-3x } & = & 15 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-15}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+13x } & = & -2 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &22x & = &13\\\Leftrightarrow & \color{red}{22}x & = &13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{13}{22} } & & \\ & V = \left\{ \frac{13}{22} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & 15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-6}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-4x } & = & -8 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+9}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-7x } & = & -2 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)