Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+9}& = & -9 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-2x } & = & -9 \color{red}{ +2x }\color{blue}{-9-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-x & = &-18\\\Leftrightarrow & \color{red}{-}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-18}{-1} \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & 13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-1}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-5x } & = & 8 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+6}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-11x } & = & -5 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-21x & = &-11\\\Leftrightarrow & \color{red}{-21}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-11}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{11}{21} } & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+5}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+9x } & = & 5 \color{red}{ -9x }\color{blue}{-5+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+11}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-9x } & = & 10 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+12}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+11x } & = & 4 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &20x & = &-8\\\Leftrightarrow & \color{red}{20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+7}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+13x } & = & -1 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &27x & = &-8\\\Leftrightarrow & \color{red}{27}x & = &-8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{27} } & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & 15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 15 \color{blue}{-14} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-9}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-8x } & = & 15 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)