Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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