Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+8}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-9x } & = & -1 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &13x & = &-20\\\Leftrightarrow & \color{red}{13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & 5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-x } & = & 6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+3}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-10x } & = & -4 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-23x & = &-7\\\Leftrightarrow & \color{red}{-23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-14}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+13x } & = & 14 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &22x & = &28\\\Leftrightarrow & \color{red}{22}x & = &28\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{28}{22} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+11}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-9x } & = & -10 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)