Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+15}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-7x } & = & -6 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-21\\\Leftrightarrow & \color{red}{-17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-3}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-7x } & = & -14 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x } & = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & 1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-15}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-3x } & = & -3 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &10x & = &12\\\Leftrightarrow & \color{red}{10}x & = &12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+2}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2+11x } & = & 8 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &25x & = &6\\\Leftrightarrow & \color{red}{25}x & = &6\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{6}{25} \\\Leftrightarrow & \color{green}{ x = \frac{6}{25} } & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+7}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-9x } & = & 1 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+8}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-13x } & = & -1 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-28x & = &-9\\\Leftrightarrow & \color{red}{-28}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{28} } & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)