Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+15}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-7x } & = & -1 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+13}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-13x } & = & 14 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-8}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8+5x } & = & 6 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-14}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x } & = & 2 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+1}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1+2x } & = & 8 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+6}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+5x } & = & 2 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-7}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-14x } & = & -7 \color{red}{ +14x }\color{blue}{+7-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & 14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-4x & = &26\\\Leftrightarrow & \color{red}{-4}x & = &26\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{26}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)