Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-11}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+3x } & = & 7 \color{red}{ -3x }\color{blue}{+11+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &13x & = &18\\\Leftrightarrow & \color{red}{13}x & = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-13}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x } & = & -5 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &8x & = &8\\\Leftrightarrow & \color{red}{8}x & = &8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{8}{8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-2}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-11x } & = & 7 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+14}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-8x } & = & 13 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-5}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-11x } & = & 1 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-5}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+13x } & = & 2 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &24x & = &7\\\Leftrightarrow & \color{red}{24}x & = &7\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{7}{24} \\\Leftrightarrow & \color{green}{ x = \frac{7}{24} } & & \\ & V = \left\{ \frac{7}{24} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-5}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5-5x } & = & -10 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-x } & = & 4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &7x & = &18\\\Leftrightarrow & \color{red}{7}x & = &18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-x } & = & -12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)