Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &10x & = &18\\\Leftrightarrow & \color{red}{10}x & = &18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-1}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1-5x } & = & -8 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-10}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-9x } & = & 4 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-8}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-13x } & = & 8 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-2x & = &16\\\Leftrightarrow & \color{red}{-2}x & = &16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{16}{-2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+9}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-5x } & = & -12 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &7x & = &-21\\\Leftrightarrow & \color{red}{7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-21}{7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+7}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-3x } & = & 9 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-9}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+11x } & = & 13 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &15x & = &22\\\Leftrightarrow & \color{red}{15}x & = &22\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{22}{15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+12}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12+3x } & = & 9 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)