Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-3}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+14x } & = & -15 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+14}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & 4 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+12}& = & 15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12+6x } & = & 15 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &19x & = &3\\\Leftrightarrow & \color{red}{19}x & = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-3}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-13x } & = & -7 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-12}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-4x } & = & -15 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x } & = & -9 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+6}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+8x } & = & 5 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-3}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-13x } & = & -8 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-x } & = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &x & = &29\\\Leftrightarrow & \color{red}{}x & = &29\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 29 \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)