Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & 2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-1}& = & -4 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+15x } & = & -4 \color{red}{ -15x }\color{blue}{+1+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x } & = & -2 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &25x & = &1\\\Leftrightarrow & \color{red}{25}x & = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-26\\\Leftrightarrow & \color{red}{-6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & 15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+1}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-11x } & = & 10 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-1}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-13x } & = & -4 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-2}& = & -1 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-2x } & = & -1 \color{red}{ +2x }\color{blue}{+2-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & -1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-13}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-11x } & = & 11 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-21x & = &24\\\Leftrightarrow & \color{red}{-21}x & = &24\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{24}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-9}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+13x } & = & -8 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &21x & = &1\\\Leftrightarrow & \color{red}{21}x & = &1\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{1}{21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)