Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & -9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+11}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+7x } & = & 2 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-11}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+4x } & = & -1 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+1}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-9x } & = & 6 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-10}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-4x } & = & -1 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-1}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1+6x } & = & 6 \color{red}{ -6x }\color{blue}{+1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+7}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+10x } & = & 11 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &21x & = &4\\\Leftrightarrow & \color{red}{21}x & = &4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-6}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+7x } & = & -12 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)