Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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