Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+3}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-9x } & = & 10 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-7}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-4x } & = & -3 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-27\\\Leftrightarrow & \color{red}{-8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-8x & = &18\\\Leftrightarrow & \color{red}{-8}x & = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-14}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+11x } & = & -13 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &25x & = &1\\\Leftrightarrow & \color{red}{25}x & = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-2}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-13x } & = & -7 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-28x & = &-5\\\Leftrightarrow & \color{red}{-28}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{28} } & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+13}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-9x } & = & 4 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-10}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+3x } & = & 13 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-x } & = & 6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)