Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-11}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+2x } & = & -12 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+15}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-13x } & = & -8 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-23\\\Leftrightarrow & \color{red}{-14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-15}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-14x } & = & 11 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-5x & = &26\\\Leftrightarrow & \color{red}{-5}x & = &26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{5} } & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+1}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-4x } & = & 9 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -9 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-7}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+4x } & = & -12 \color{red}{ -4x }\color{blue}{+7+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+7}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-11x } & = & 5 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+2}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-7x } & = & -3 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+4}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+7x } & = & -15 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &18x & = &-19\\\Leftrightarrow & \color{red}{18}x & = &-19\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-19}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{18} } & & \\ & V = \left\{ \frac{-19}{18} \right\} & \\\end{align}\)