Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-1}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+13x } & = & 3 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &20x & = &4\\\Leftrightarrow & \color{red}{20}x & = &4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-13}& = & -9 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-6x } & = & -9 \color{red}{ +6x }\color{blue}{+13-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+7}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+5x } & = & 5 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-14}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-6x } & = & 11 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &5x & = &25\\\Leftrightarrow & \color{red}{5}x & = &25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{25}{5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+2}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-11x } & = & 4 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-1}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-7x } & = & 12 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & 11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-4}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-5x } & = & -8 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+3}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3+3x } & = & 3 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)