Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+11}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-7x } & = & 12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+1}& = & -6 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+4x } & = & -6 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-4}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-9x } & = & -7 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-2x & = &-3\\\Leftrightarrow & \color{red}{-2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-11}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11-4x } & = & -5 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+6}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+2x } & = & 12 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-7}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+9x } & = & -2 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-4}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-10x } & = & -8 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+1}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-13x } & = & -15 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-x } & = & -8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-11}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-14x } & = & -14 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)