Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-6x+4=-8+x\)
2. \(15x+6=-4+2x\)
3. \(-3x-8=-9+x\)
4. \(-15x-14=-7+13x\)
5. \(7x-15=4-3x\)
6. \(-5x+4=-6+x\)
7. \(12x+13=11+5x\)
8. \(11x+5=15-10x\)
9. \(10x-15=-8-9x\)
10. \(5x-5=4+8x\)
11. \(x-9=-8+0x\)
12. \(-11x+14=2+14x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+6}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-2x } & = & -4 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & -9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-14}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-13x } & = & -7 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-28x & = &7\\\Leftrightarrow & \color{red}{-28}x & = &7\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{7}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-15}& = & 4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+3x } & = & 4 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+13}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-5x } & = & 11 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+5}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+10x } & = & 15 \color{red}{ -10x }\color{blue}{-5+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &21x & = &10\\\Leftrightarrow & \color{red}{21}x & = &10\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{10}{21} \\\Leftrightarrow & \color{green}{ x = \frac{10}{21} } & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-15}& = & -8 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+9x } & = & -8 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-5}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-8x } & = & 4 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-9}& = & -8 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+0x } & = & -8 \color{red}{ +0x }\color{blue}{+9+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+14}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-14x } & = & 2 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)