Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-x } & = & -6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-26\\\Leftrightarrow & \color{red}{-13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-26}{-13} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+2}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-7x } & = & -4 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+3}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-7x } & = & -5 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+3}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-13x } & = & -7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+7}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-4x } & = & 13 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+12}& = & 15 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-6x } & = & 15 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-13}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-10x } & = & 11 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &3x & = &24\\\Leftrightarrow & \color{red}{3}x & = &24\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{24}{3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-11}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-11x } & = & 14 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-16x & = &25\\\Leftrightarrow & \color{red}{-16}x & = &25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{16} } & & \\ & V = \left\{ \frac{-25}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)