Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-6}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+9x } & = & 8 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &14x & = &14\\\Leftrightarrow & \color{red}{14}x & = &14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{14}{14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-2}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2+5x } & = & 7 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-x } & = & -15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-13}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-3x } & = & 14 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &x & = &27\\\Leftrightarrow & \color{red}{}x & = &27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 27 \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+15}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-5x } & = & -14 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &9x & = &-29\\\Leftrightarrow & \color{red}{9}x & = &-29\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-29}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{9} } & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-13x } & = & 4 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-8}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+13x } & = & 3 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &23x & = &11\\\Leftrightarrow & \color{red}{23}x & = &11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-6}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-11x } & = & -4 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+8}& = & -13 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-12x } & = & -13 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & -11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-20\\\Leftrightarrow & \color{red}{-4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-20}{-4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)