Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+14}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+9x } & = & -4 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-11}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x } & = & -4 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-7}& = & -10 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+5x } & = & -10 \color{red}{ -5x }\color{blue}{+7+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+7}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7+13x } & = & 8 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & -8x \color{blue}{+13x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-10}& = & -13 \color{red}{ +2x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-2x } & = & -13 \color{red}{ +2x }\color{blue}{+10-2x } \\\Leftrightarrow & -9x \color{blue}{-2x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-3}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-14x } & = & 10 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-14}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14+11x } & = & -13 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & -15x \color{blue}{+11x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+6}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-2x } & = & 12 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-8}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-14x } & = & -5 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-27x & = &3\\\Leftrightarrow & \color{red}{-27}x & = &3\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{3}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+15}& = & 4 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+14x } & = & 4 \color{red}{ -14x }\color{blue}{-15+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+9}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+3x } & = & -13 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)