Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-13}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-7x } & = & 5 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-10}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-5x } & = & 4 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-13}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13+11x } & = & 11 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &17x & = &24\\\Leftrightarrow & \color{red}{17}x & = &24\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{24}{17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+4}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-8x } & = & 1 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+7}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+13x } & = & -4 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &21x & = &-11\\\Leftrightarrow & \color{red}{21}x & = &-11\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-11}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{21} } & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-11}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-4x } & = & -8 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-5}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-9x } & = & 8 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-10}& = & 1 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+15x } & = & 1 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &28x & = &11\\\Leftrightarrow & \color{red}{28}x & = &11\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{11}{28} \\\Leftrightarrow & \color{green}{ x = \frac{11}{28} } & & \\ & V = \left\{ \frac{11}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+13}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13+13x } & = & -3 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &27x & = &-16\\\Leftrightarrow & \color{red}{27}x & = &-16\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-16}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{27} } & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-14}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14+7x } & = & -13 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-15}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-5x } & = & 13 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &x & = &28\\\Leftrightarrow & \color{red}{}x & = &28\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 28 \\\Leftrightarrow & \color{green}{ x = 28 } & & \\ & V = \left\{ 28 \right\} & \\\end{align}\)