Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-2}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+7x } & = & -13 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-2}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-6x } & = & 2 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+15}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-14x } & = & 3 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-12\\\Leftrightarrow & \color{red}{-23}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-12}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{12}{23} } & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+15}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-5x } & = & -10 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-25\\\Leftrightarrow & \color{red}{-17}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-25}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{25}{17} } & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-2}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+13x } & = & -11 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &24x & = &-9\\\Leftrightarrow & \color{red}{24}x & = &-9\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-9}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+4}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & -2 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-9x & = &28\\\Leftrightarrow & \color{red}{-9}x & = &28\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{28}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{9} } & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-5}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-4x } & = & 8 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+6}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-7x } & = & 5 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-x } & = & 10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)