Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+6}& = & -11 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+x } & = & -11 \color{red}{ -x }\color{blue}{-6+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &2x & = &-17\\\Leftrightarrow & \color{red}{2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-5}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-11x } & = & -7 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-25\\\Leftrightarrow & \color{red}{-3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+9}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+7x } & = & -14 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &6x & = &-23\\\Leftrightarrow & \color{red}{6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-23}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & 5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+10}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-4x } & = & 11 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+13}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-7x } & = & -1 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-24\\\Leftrightarrow & \color{red}{-4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-24}{-4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-4}& = & -14 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+12x } & = & -14 \color{red}{ -12x }\color{blue}{+4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+13}& = & -15 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13-2x } & = & -15 \color{red}{ +2x }\color{blue}{-13-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &11x & = &-28\\\Leftrightarrow & \color{red}{11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)