Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+9}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-2x } & = & 8 \color{red}{ +2x }\color{blue}{-9-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+2}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-7x } & = & -3 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-5\\\Leftrightarrow & \color{red}{-17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+13}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-9x } & = & 2 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+7}& = & -14 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+5x } & = & -14 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &16x & = &-21\\\Leftrightarrow & \color{red}{16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-21}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{16} } & & \\ & V = \left\{ \frac{-21}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-7}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-5x } & = & -8 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-26\\\Leftrightarrow & \color{red}{-16}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-26}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+6}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-9x } & = & -11 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-2x & = &-17\\\Leftrightarrow & \color{red}{-2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-x } & = & 14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-13}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-5x } & = & 11 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &6x & = &24\\\Leftrightarrow & \color{red}{6}x & = &24\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{24}{6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+8}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+6x } & = & -1 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)