Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-14}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x } & = & -3 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &3x & = &11\\\Leftrightarrow & \color{red}{3}x & = &11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-15}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+11x } & = & -3 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+13}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-3x } & = & 5 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-5}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-3x } & = & 11 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-15}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-13x } & = & -10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-25x & = &5\\\Leftrightarrow & \color{red}{-25}x & = &5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+14}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & 9 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-7}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-8x } & = & 11 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+14}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-14x } & = & -1 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-27x & = &-15\\\Leftrightarrow & \color{red}{-27}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-15}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-1}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-9x } & = & 8 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+4}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-11x } & = & 12 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)