Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-10}& = & -8 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10+14x } & = & -8 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-7}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+11x } & = & -6 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &26x & = &1\\\Leftrightarrow & \color{red}{26}x & = &1\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{1}{26} \\\Leftrightarrow & \color{green}{ x = \frac{1}{26} } & & \\ & V = \left\{ \frac{1}{26} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-15x & = &26\\\Leftrightarrow & \color{red}{-15}x & = &26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+15}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-11x } & = & 14 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-7}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+3x } & = & -3 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)