Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-1}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-8x } & = & -10 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-23x & = &-9\\\Leftrightarrow & \color{red}{-23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-5}& = & 13 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+10x } & = & 13 \color{red}{ -10x }\color{blue}{+5+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &21x & = &18\\\Leftrightarrow & \color{red}{21}x & = &18\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{18}{21} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+11}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-5x } & = & -8 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-3}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+13x } & = & -5 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-x } & = & -8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-22\\\Leftrightarrow & \color{red}{-14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-12}& = & 7 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-6x } & = & 7 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-14}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-10x } & = & 3 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-12}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-4x } & = & 14 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-7x & = &26\\\Leftrightarrow & \color{red}{-7}x & = &26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)