Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+6}& = & 12 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+8x } & = & 12 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+14}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+8x } & = & -13 \color{red}{ -8x }\color{blue}{-14+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &11x & = &-27\\\Leftrightarrow & \color{red}{11}x & = &-27\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-27}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{11} } & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+5}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-3x } & = & -15 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &10x & = &-20\\\Leftrightarrow & \color{red}{10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-20}{10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+13}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-6x } & = & 10 \color{red}{ +6x }\color{blue}{-13-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-x } & = & 8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+7}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+7x } & = & 1 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-10}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-7x } & = & 13 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+8}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-4x } & = & -10 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-18\\\Leftrightarrow & \color{red}{-19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+15}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-13x } & = & -8 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-23\\\Leftrightarrow & \color{red}{-4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-3}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-10x } & = & 10 \color{red}{ +10x }\color{blue}{+3-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+12}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-14x } & = & 12 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-25x & = &0\\\Leftrightarrow & \color{red}{-25}x & = &0\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{0}{-25} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)