Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-15}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-13x } & = & -10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &2x & = &5\\\Leftrightarrow & \color{red}{2}x & = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-11x & = &24\\\Leftrightarrow & \color{red}{-11}x & = &24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+14}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & 11 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-3\\\Leftrightarrow & \color{red}{-25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x } & = & -7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+11}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+2x } & = & -1 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+1}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-7x } & = & 11 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-5}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-7x } & = & -1 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+10}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+13x } & = & 14 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &21x & = &4\\\Leftrightarrow & \color{red}{21}x & = &4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &6x & = &-9\\\Leftrightarrow & \color{red}{6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & 15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)