Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-8}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+11x } & = & -13 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-x } & = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-14}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+13x } & = & -1 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &27x & = &13\\\Leftrightarrow & \color{red}{27}x & = &13\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{13}{27} \\\Leftrightarrow & \color{green}{ x = \frac{13}{27} } & & \\ & V = \left\{ \frac{13}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-16x & = &28\\\Leftrightarrow & \color{red}{-16}x & = &28\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{28}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+12}& = & 14 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+15x } & = & 14 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-13x } & = & 4 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-14}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-7x } & = & 14 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-13x & = &28\\\Leftrightarrow & \color{red}{-13}x & = &28\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{28}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{13} } & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+1}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-11x } & = & -12 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & -15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-23\\\Leftrightarrow & \color{red}{-10}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+15}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+3x } & = & 1 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &2x & = &-14\\\Leftrightarrow & \color{red}{2}x & = &-14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-14}{2} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)