Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-2}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & 8 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+13}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-5x } & = & -11 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-24\\\Leftrightarrow & \color{red}{-14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-x } & = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-19\\\Leftrightarrow & \color{red}{-8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7-x } & = & 3 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+7}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-5x } & = & -9 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-9}& = & -5 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+15x } & = & -5 \color{red}{ -15x }\color{blue}{+9+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+10}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+13x } & = & 12 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &22x & = &2\\\Leftrightarrow & \color{red}{22}x & = &2\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{2}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-15}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-8x } & = & -2 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & 10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-5}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+2x } & = & 9 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)