Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-3x-8=-7+x\)
2. \(-x+11=13+0x\)
3. \(11x+6=12-10x\)
4. \(-6x-5=-3+13x\)
5. \(-7x+2=-2+x\)
6. \(-8x-13=10+9x\)
7. \(-2x-13=10+x\)
8. \(-2x-10=11+x\)
9. \(-12x+14=1+x\)
10. \(-12x+9=4+13x\)
11. \(13x+8=5-4x\)
12. \(3x-14=-9+4x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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