Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-5x+3=2+x\)
2. \(10x-10=10+7x\)
3. \(-6x-13=6+13x\)
4. \(-7x+14=9+x\)
5. \(-5x-1=3+x\)
6. \(-9x-13=-2+14x\)
7. \(12x+3=5-11x\)
8. \(5x+4=15-2x\)
9. \(-7x-8=-7+8x\)
10. \(x-3=-14-8x\)
11. \(8x-6=4+3x\)
12. \(-x+11=-1+0x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-10}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-7x } & = & 10 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-13}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-13x } & = & 6 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-19x & = &19\\\Leftrightarrow & \color{red}{-19}x & = &19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{19}{-19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-13}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-14x } & = & -2 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-23x & = &11\\\Leftrightarrow & \color{red}{-23}x & = &11\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{11}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+3}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3+11x } & = & 5 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+4}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4+2x } & = & 15 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-8}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-8x } & = & -7 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-3}& = & -14 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+8x } & = & -14 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-6}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-3x } & = & 4 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+11}& = & -1 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+0x } & = & -1 \color{red}{ +0x }\color{blue}{-11+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)