Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+8}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-2x } & = & -12 \color{red}{ +2x }\color{blue}{-8-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-5}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -15 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-x } & = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &9x & = &17\\\Leftrightarrow & \color{red}{9}x & = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-10}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-5x } & = & -4 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-3}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-11x } & = & 12 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+10}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10+2x } & = & -6 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+1}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-6x } & = & 12 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-x & = &11\\\Leftrightarrow & \color{red}{-}x & = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+10}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+11x } & = & -13 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &25x & = &-23\\\Leftrightarrow & \color{red}{25}x & = &-23\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-23}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-3}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-7x } & = & 11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)