Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-1}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-7x } & = & -6 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & -7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+4}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+4x } & = & -12 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-11}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+13x } & = & 13 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &23x & = &24\\\Leftrightarrow & \color{red}{23}x & = &24\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{24}{23} \\\Leftrightarrow & \color{green}{ x = \frac{24}{23} } & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+8}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+6x } & = & -5 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &19x & = &-13\\\Leftrightarrow & \color{red}{19}x & = &-13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+11}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & 2 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-20x & = &-9\\\Leftrightarrow & \color{red}{-20}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-9}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{20} } & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+5}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-14x } & = & 7 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-25x & = &2\\\Leftrightarrow & \color{red}{-25}x & = &2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{25} } & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+10}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-8x } & = & 13 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-12}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-9x } & = & -4 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+5}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-7x } & = & 1 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)