Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+12}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-13x } & = & -2 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-13}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+7x } & = & 12 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &22x & = &25\\\Leftrightarrow & \color{red}{22}x & = &25\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{25}{22} \\\Leftrightarrow & \color{green}{ x = \frac{25}{22} } & & \\ & V = \left\{ \frac{25}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & 1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-12}& = & 1 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+x } & = & 1 \color{red}{ -x }\color{blue}{+12+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-9}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-2x } & = & -10 \color{red}{ +2x }\color{blue}{+9-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 5 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-x } & = & 7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-13}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+7x } & = & -6 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)