Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+2}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-10x } & = & 13 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-19x & = &11\\\Leftrightarrow & \color{red}{-19}x & = &11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-2}& = & 7 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-6x } & = & 7 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+10}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-13x } & = & -3 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-25x & = &-13\\\Leftrightarrow & \color{red}{-25}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-9\\\Leftrightarrow & \color{red}{-15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-11}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-7x } & = & 10 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-17x & = &21\\\Leftrightarrow & \color{red}{-17}x & = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-1}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-13x } & = & 13 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-8}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x } & = & -15 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+14}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+13x } & = & -5 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &12x & = &-19\\\Leftrightarrow & \color{red}{12}x & = &-19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+9}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9+7x } & = & -4 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &15x & = &-13\\\Leftrightarrow & \color{red}{15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+15}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+11x } & = & 10 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)