Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+4}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-10x } & = & -6 \color{red}{ +10x }\color{blue}{-4-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-10x & = &23\\\Leftrightarrow & \color{red}{-10}x & = &23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{10} } & & \\ & V = \left\{ \frac{-23}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-11}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11+11x } & = & -1 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-23\\\Leftrightarrow & \color{red}{-11}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-4}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+11x } & = & 8 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+9}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-7x } & = & 6 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+11}& = & -12 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-6x } & = & -12 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &7x & = &-23\\\Leftrightarrow & \color{red}{7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-11}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-13x } & = & -11 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+9}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+3x } & = & 12 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+3}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-9x } & = & -9 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-22x & = &-12\\\Leftrightarrow & \color{red}{-22}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-12}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)