Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+12}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+7x } & = & -1 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &15x & = &-13\\\Leftrightarrow & \color{red}{15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-5}& = & -8 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+14x } & = & -8 \color{red}{ -14x }\color{blue}{+5+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-7}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-13x } & = & 11 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-28x & = &18\\\Leftrightarrow & \color{red}{-28}x & = &18\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{18}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-2}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2+11x } & = & 9 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-4}& = & -5 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+8x } & = & -5 \color{red}{ -8x }\color{blue}{+4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+5}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-5x } & = & -7 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-3}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-6x } & = & 10 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & -2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &-10x & = &12\\\Leftrightarrow & \color{red}{-10}x & = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-5}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & -9 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)