Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & 3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+15}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+2x } & = & -15 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &9x & = &-30\\\Leftrightarrow & \color{red}{9}x & = &-30\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-30}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+14}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & 13 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-10}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-x } & = & -4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-12}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-7x } & = & -4 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-5}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5+11x } & = & -9 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-6}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-5x } & = & 4 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+12}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-7x } & = & -12 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-24\\\Leftrightarrow & \color{red}{-17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+7}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-9x } & = & 3 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-12}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-13x } & = & 13 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)