Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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