Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & 12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & -1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-10}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-13x } & = & -12 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+6}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6-11x } & = & -3 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & -11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-23\\\Leftrightarrow & \color{red}{-15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+11}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11-13x } & = & 7 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &2x & = &-4\\\Leftrightarrow & \color{red}{2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-4}{2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+7}& = & 13 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+9x } & = & 13 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & 1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+14}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+7x } & = & 13 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+5}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5+5x } & = & 11 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)