Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-10}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-4x } & = & -12 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-6}& = & 6 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+15x } & = & 6 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &16x & = &12\\\Leftrightarrow & \color{red}{16}x & = &12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-8}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-6x } & = & -1 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-7}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-13x } & = & -10 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-4}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-11x } & = & 14 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-19x & = &18\\\Leftrightarrow & \color{red}{-19}x & = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-12}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-14x } & = & -12 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)