Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & 15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-9x & = &27\\\Leftrightarrow & \color{red}{-9}x & = &27\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{27}{-9} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-7}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-11x } & = & 7 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-3}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-6x } & = & 8 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-x & = &11\\\Leftrightarrow & \color{red}{-}x & = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+15}& = & 3 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-2x } & = & 3 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+13}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+3x } & = & -15 \color{red}{ -3x }\color{blue}{-13+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &7x & = &-28\\\Leftrightarrow & \color{red}{7}x & = &-28\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-28}{7} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-11}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-14x } & = & 1 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+6}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-13x } & = & 8 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & -14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)