Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-4}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-9x } & = & -5 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+8}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-13x } & = & -2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-7}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-5x } & = & -7 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-2}& = & 6 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+14x } & = & 6 \color{red}{ -14x }\color{blue}{+2+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &17x & = &8\\\Leftrightarrow & \color{red}{17}x & = &8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-x } & = & -1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &3x & = &11\\\Leftrightarrow & \color{red}{3}x & = &11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+12}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+13x } & = & -9 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &20x & = &-21\\\Leftrightarrow & \color{red}{20}x & = &-21\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-21}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{20} } & & \\ & V = \left\{ \frac{-21}{20} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-2}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-3x } & = & 12 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+8}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-7x } & = & -11 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & 12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)