Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+2}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-8x } & = & 13 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-x } & = & -2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+11}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-5x } & = & -15 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-26\\\Leftrightarrow & \color{red}{-17}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-26}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+6}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-8x } & = & 6 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-13x } & = & 13 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-18x & = &26\\\Leftrightarrow & \color{red}{-18}x & = &26\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{26}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-14}& = & 4 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+14x } & = & 4 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &29x & = &18\\\Leftrightarrow & \color{red}{29}x & = &18\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{18}{29} \\\Leftrightarrow & \color{green}{ x = \frac{18}{29} } & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & -8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-11}& = & -2 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+10x } & = & -2 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+9}& = & 6 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9+4x } & = & 6 \color{red}{ -4x }\color{blue}{-9+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & 7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-14x & = &14\\\Leftrightarrow & \color{red}{-14}x & = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)