Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-11}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-9x } & = & -13 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-20x & = &-2\\\Leftrightarrow & \color{red}{-20}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-4}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+7x } & = & -6 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+1}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+11x } & = & 1 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-6}& = & -7 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+9x } & = & -7 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+11}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-8x } & = & -10 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-21\\\Leftrightarrow & \color{red}{-15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-7}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -14 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-20x & = &-7\\\Leftrightarrow & \color{red}{-20}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-7}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{20} } & & \\ & V = \left\{ \frac{7}{20} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+3}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+11x } & = & 2 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)