Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-1}& = & -10 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+14x } & = & -10 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-15}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-5x } & = & -13 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+6}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+11x } & = & 1 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+10}& = & -10 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+12x } & = & -10 \color{red}{ -12x }\color{blue}{-10+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &25x & = &-20\\\Leftrightarrow & \color{red}{25}x & = &-20\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-20}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-7}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & -7 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x } & = & -7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &13x & = &-20\\\Leftrightarrow & \color{red}{13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+11}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-10x } & = & 10 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-5}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+11x } & = & -11 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-x } & = & 1 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+4}& = & -11 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+2x } & = & -11 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+7}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+13x } & = & 6 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &24x & = &-1\\\Leftrightarrow & \color{red}{24}x & = &-1\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-1}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{24} } & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)