Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-16x & = &18\\\Leftrightarrow & \color{red}{-16}x & = &18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-1}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1-6x } & = & -15 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-x & = &-14\\\Leftrightarrow & \color{red}{-}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-14}{-1} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+13}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-5x } & = & -9 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-22\\\Leftrightarrow & \color{red}{-14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+9}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9-9x } & = & -15 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-x } & = & -1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+3}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3+7x } & = & 15 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+1}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+5x } & = & -2 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)