Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-5}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5+11x } & = & 12 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &23x & = &17\\\Leftrightarrow & \color{red}{23}x & = &17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-4}& = & -4 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+15x } & = & -4 \color{red}{ -15x }\color{blue}{+4+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+8}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+9x } & = & -3 \color{red}{ -9x }\color{blue}{-8+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+5}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-7x } & = & -3 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-20x & = &-8\\\Leftrightarrow & \color{red}{-20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-8}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-7x } & = & 1 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-12}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-8x } & = & -11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)