Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & 1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &-4x & = &15\\\Leftrightarrow & \color{red}{-4}x & = &15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & -1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+14}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+7x } & = & -1 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &19x & = &-15\\\Leftrightarrow & \color{red}{19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+3}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-9x } & = & -9 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-3}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-7x } & = & -11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-3}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-13x } & = & 10 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-15}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & 3 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+13}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+11x } & = & -4 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &17x & = &-17\\\Leftrightarrow & \color{red}{17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-17}{17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-13}& = & 13 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+4x } & = & 13 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &9x & = &26\\\Leftrightarrow & \color{red}{9}x & = &26\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{26}{9} \\\Leftrightarrow & \color{green}{ x = \frac{26}{9} } & & \\ & V = \left\{ \frac{26}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-1}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-7x } & = & 7 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &2x & = &8\\\Leftrightarrow & \color{red}{2}x & = &8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{8}{2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)