Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+2}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+11x } & = & 8 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &20x & = &6\\\Leftrightarrow & \color{red}{20}x & = &6\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{6}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+6}& = & 6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+15x } & = & 6 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-9}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-11x } & = & -8 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+9}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-9x } & = & -12 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &2x & = &-21\\\Leftrightarrow & \color{red}{2}x & = &-21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+10}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+12x } & = & -3 \color{red}{ -12x }\color{blue}{-10+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &25x & = &-13\\\Leftrightarrow & \color{red}{25}x & = &-13\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-13}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{25} } & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-12}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+4x } & = & -2 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-12}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-8x } & = & -8 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-x } & = & -1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &11x & = &-12\\\Leftrightarrow & \color{red}{11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & -4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-13}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-9x } & = & -12 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)