Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+4}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & -14 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-18\\\Leftrightarrow & \color{red}{-25}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-18}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{18}{25} } & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-11}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-8x } & = & -11 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+13}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-11x } & = & 15 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-5}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+5x } & = & -1 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & -3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-14}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-11x } & = & -14 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-7}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & -10 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-9}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-14x } & = & -2 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & 12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)