Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+13}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & -11 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &19x & = &-24\\\Leftrightarrow & \color{red}{19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-6}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+8x } & = & -15 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-7}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+2x } & = & 13 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-9}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-9x } & = & 1 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x } & = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-11}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-5x } & = & 6 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-19x & = &17\\\Leftrightarrow & \color{red}{-19}x & = &17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+7}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7+5x } & = & 13 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-6}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-13x } & = & 4 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-6}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-4x } & = & 5 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-2}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-7x } & = & 14 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-17x & = &16\\\Leftrightarrow & \color{red}{-17}x & = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)