Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+8}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-9x } & = & 10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-5}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x } & = & 11 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+4}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & -6 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &15x & = &-10\\\Leftrightarrow & \color{red}{15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+2}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+7x } & = & -8 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-x } & = & 4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & -15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+3}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+13x } & = & 9 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &23x & = &6\\\Leftrightarrow & \color{red}{23}x & = &6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)