Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-5}& = & 11 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+8x } & = & 11 \color{red}{ -8x }\color{blue}{+5+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-1}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-7x } & = & 13 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-4}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-11x } & = & -2 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-12}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-2x } & = & 12 \color{red}{ +2x }\color{blue}{+12-2x } \\\Leftrightarrow & -15x \color{blue}{-2x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-17x & = &24\\\Leftrightarrow & \color{red}{-17}x & = &24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{17} } & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-7}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-7x } & = & -15 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-6}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-5x } & = & -13 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-14}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-3x } & = & -14 \color{red}{ +3x }\color{blue}{+14-3x } \\\Leftrightarrow & -10x \color{blue}{-3x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-3}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-4x } & = & 4 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & -13x \color{blue}{-4x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+7}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-11x } & = & 9 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+4}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4-11x } & = & -2 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)