Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+7}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-10x } & = & -1 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+5}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x } & = & 1 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-13}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-13x } & = & 15 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-19x & = &28\\\Leftrightarrow & \color{red}{-19}x & = &28\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{28}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{19} } & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-3}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-4x } & = & -7 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+8}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-7x } & = & -2 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+9}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+6x } & = & -5 \color{red}{ -6x }\color{blue}{-9+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &5x & = &-14\\\Leftrightarrow & \color{red}{5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)