Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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