Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+8}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-8x } & = & 5 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-9}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-13x } & = & -13 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+11}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+7x } & = & 12 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-13}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-9x } & = & -1 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-6}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6+9x } & = & 10 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &23x & = &16\\\Leftrightarrow & \color{red}{23}x & = &16\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{16}{23} \\\Leftrightarrow & \color{green}{ x = \frac{16}{23} } & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-15}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15-8x } & = & 15 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-9x & = &30\\\Leftrightarrow & \color{red}{-9}x & = &30\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{30}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-14}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+5x } & = & -9 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+6}& = & 13 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+15x } & = & 13 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &23x & = &7\\\Leftrightarrow & \color{red}{23}x & = &7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)