Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+7}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-9x } & = & 10 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+9}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+13x } & = & 15 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &24x & = &6\\\Leftrightarrow & \color{red}{24}x & = &6\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{6}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+7}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+15x } & = & 4 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &16x & = &-3\\\Leftrightarrow & \color{red}{16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-3}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-14}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-9x } & = & -7 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+1}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-5x } & = & 11 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+10}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-13x } & = & -8 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-18\\\Leftrightarrow & \color{red}{-16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-15}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15+11x } & = & 14 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &10x & = &29\\\Leftrightarrow & \color{red}{10}x & = &29\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{29}{10} \\\Leftrightarrow & \color{green}{ x = \frac{29}{10} } & & \\ & V = \left\{ \frac{29}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+11}& = & -8 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-6x } & = & -8 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &7x & = &-19\\\Leftrightarrow & \color{red}{7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-3}& = & -1 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+8x } & = & -1 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)