Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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