Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-13x & = &24\\\Leftrightarrow & \color{red}{-13}x & = &24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+10}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10-9x } & = & -10 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-6}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-11x } & = & -15 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-21x & = &-9\\\Leftrightarrow & \color{red}{-21}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-9}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+11}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+2x } & = & -1 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-10}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-5x } & = & 4 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+13}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-3x } & = & 9 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-13}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-8x } & = & 9 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &3x & = &22\\\Leftrightarrow & \color{red}{3}x & = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+8}& = & -7 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-15x } & = & -7 \color{red}{ +15x }\color{blue}{-8-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-15\\\Leftrightarrow & \color{red}{-16}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{15}{16} } & & \\ & V = \left\{ \frac{15}{16} \right\} & \\\end{align}\)