Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-5x-9=5+x\)
2. \(-9x+5=-7+7x\)
3. \(-2x-9=12+x\)
4. \(x+10=-10+0x\)
5. \(-9x-8=15+x\)
6. \(9x+7=13+7x\)
7. \(x-9=11-3x\)
8. \(-14x-11=7+x\)
9. \(3x-13=-6-11x\)
10. \(-3x-4=-8+x\)
11. \(6x+12=3-5x\)
12. \(-8x+14=-5+9x\)

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+5}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-7x } & = & -7 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+10}& = & -10 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+0x } & = & -10 \color{red}{ +0x }\color{blue}{-10+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-10x & = &23\\\Leftrightarrow & \color{red}{-10}x & = &23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{10} } & & \\ & V = \left\{ \frac{-23}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+7}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7-7x } & = & 13 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-9}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+3x } & = & 11 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &4x & = &20\\\Leftrightarrow & \color{red}{4}x & = &20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{20}{4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-13}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+11x } & = & -6 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &14x & = &7\\\Leftrightarrow & \color{red}{14}x & = &7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-x } & = & -8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+12}& = & 3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x } & = & 3 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+14}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x } & = & -5 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-19\\\Leftrightarrow & \color{red}{-17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)