Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+10}& = & -10 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+10x } & = & -10 \color{red}{ -10x }\color{blue}{-10+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+9}& = & -13 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-12x } & = & -13 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-9}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-13x } & = & -8 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-15}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+8x } & = & 8 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &19x & = &23\\\Leftrightarrow & \color{red}{19}x & = &23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{23}{19} } & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-3}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x } & = & -1 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-2}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-13x } & = & 15 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-28x & = &17\\\Leftrightarrow & \color{red}{-28}x & = &17\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{17}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{28} } & & \\ & V = \left\{ \frac{-17}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-14}& = & -3 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14+15x } & = & -3 \color{red}{ -15x }\color{blue}{+14+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &19x & = &11\\\Leftrightarrow & \color{red}{19}x & = &11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-2}& = & -6 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2+6x } & = & -6 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+6}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-5x } & = & -6 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+5}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5+2x } & = & 3 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+6}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-11x } & = & 5 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+1}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-10x } & = & -13 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-19x & = &-14\\\Leftrightarrow & \color{red}{-19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)