Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-11}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11+11x } & = & 10 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &15x & = &21\\\Leftrightarrow & \color{red}{15}x & = &21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-13}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-3x } & = & 12 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-4x & = &25\\\Leftrightarrow & \color{red}{-4}x & = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-10}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-3x } & = & 12 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+5}& = & -5 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5+14x } & = & -5 \color{red}{ -14x }\color{blue}{-5+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-7}& = & 14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+15x } & = & 14 \color{red}{ -15x }\color{blue}{+7+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &23x & = &21\\\Leftrightarrow & \color{red}{23}x & = &21\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{21}{23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-12}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+6x } & = & -12 \color{red}{ -6x }\color{blue}{+12+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-4}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4+13x } & = & -11 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-8}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-7x } & = & -13 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-20x & = &-5\\\Leftrightarrow & \color{red}{-20}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & 6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-7}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-13x } & = & -11 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)