Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-x } & = & -15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-4}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4+4x } & = & -9 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-11}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-5x } & = & -14 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-9}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-7x } & = & 10 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-16x & = &19\\\Leftrightarrow & \color{red}{-16}x & = &19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{16} } & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-10x & = &15\\\Leftrightarrow & \color{red}{-10}x & = &15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-5}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-6x } & = & -7 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & 15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)