Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & -6 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-12}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-7x } & = & -4 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-2}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+3x } & = & 3 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-9}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-4x } & = & -8 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-8}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-5x } & = & 15 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &9x & = &23\\\Leftrightarrow & \color{red}{9}x & = &23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & -14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-12}& = & 2 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+12x } & = & 2 \color{red}{ -12x }\color{blue}{+12+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-8}& = & 8 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+3x } & = & 8 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &16x & = &16\\\Leftrightarrow & \color{red}{16}x & = &16\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{16}{16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+6}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-13x } & = & -7 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)