Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+5}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & 5 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+9}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-4x } & = & 7 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-6}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+3x } & = & 2 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-15}& = & -1 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+14x } & = & -1 \color{red}{ -14x }\color{blue}{+15+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &29x & = &14\\\Leftrightarrow & \color{red}{29}x & = &14\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{14}{29} \\\Leftrightarrow & \color{green}{ x = \frac{14}{29} } & & \\ & V = \left\{ \frac{14}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & -10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+13x } & = & 1 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+12}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+7x } & = & 4 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-11}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-14x } & = & -5 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-2}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-7x } & = & -6 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-12}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-4x } & = & -12 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)