Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-1}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-7x } & = & -10 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-20x & = &-9\\\Leftrightarrow & \color{red}{-20}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-9}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{20} } & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+1}& = & 9 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+4x } & = & 9 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+9}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+5x } & = & -2 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &16x & = &-11\\\Leftrightarrow & \color{red}{16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-11}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-13}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+11x } & = & -11 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-6}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+4x } & = & 1 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6-x } & = & 8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-8x & = &23\\\Leftrightarrow & \color{red}{-8}x & = &23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{8} } & & \\ & V = \left\{ \frac{-23}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-11x & = &24\\\Leftrightarrow & \color{red}{-11}x & = &24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &12x & = &-2\\\Leftrightarrow & \color{red}{12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)