Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+6}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-11x } & = & 6 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-12}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-5x } & = & 14 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &6x & = &26\\\Leftrightarrow & \color{red}{6}x & = &26\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{26}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+7}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+13x } & = & 5 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+10}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-4x } & = & -8 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+14}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-4x } & = & -3 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-3}& = & -9 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3+15x } & = & -9 \color{red}{ -15x }\color{blue}{+3+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+2}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-9x } & = & 11 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-15}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-9x } & = & 3 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+3}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+14x } & = & -3 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)