Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+15}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+2x } & = & 5 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-4}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-13x } & = & -11 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-x } & = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &12x & = &19\\\Leftrightarrow & \color{red}{12}x & = &19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{19}{12} } & & \\ & V = \left\{ \frac{19}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & -9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+2}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-7x } & = & -13 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+11}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-14x } & = & -15 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-26\\\Leftrightarrow & \color{red}{-3}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{26}{3} } & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-12}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-7x } & = & -10 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)