Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+12}& = & -3 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+15x } & = & -3 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &23x & = &-15\\\Leftrightarrow & \color{red}{23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+8}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-13x } & = & -13 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-21\\\Leftrightarrow & \color{red}{-19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+12}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+13x } & = & 11 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+2}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-4x } & = & -5 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-13}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13+5x } & = & -4 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-14}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-7x } & = & 3 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & -6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)