Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-8}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-11x } & = & -5 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & 5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-14x & = &13\\\Leftrightarrow & \color{red}{-14}x & = &13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+3}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-9x } & = & 5 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-3}& = & -1 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x } & = & -1 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &25x & = &2\\\Leftrightarrow & \color{red}{25}x & = &2\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{2}{25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+13}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & 3 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+5}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5+11x } & = & -10 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-13}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-5x } & = & -4 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)