Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+6}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+14x } & = & 10 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &29x & = &4\\\Leftrightarrow & \color{red}{29}x & = &4\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{4}{29} \\\Leftrightarrow & \color{green}{ x = \frac{4}{29} } & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-13x & = &24\\\Leftrightarrow & \color{red}{-13}x & = &24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+2}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & 5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & 3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-3}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-11x } & = & -15 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &3x & = &-12\\\Leftrightarrow & \color{red}{3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-12}{3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7-x } & = & -9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)