Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-15}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-11x } & = & 15 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &x & = &30\\\Leftrightarrow & \color{red}{}x & = &30\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 30 \\\Leftrightarrow & \color{green}{ x = 30 } & & \\ & V = \left\{ 30 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-6}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-6x } & = & 10 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-x } & = & 1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-10}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+6x } & = & 12 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &19x & = &22\\\Leftrightarrow & \color{red}{19}x & = &22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-12x & = &-12\\\Leftrightarrow & \color{red}{-12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-12}{-12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & -8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+10}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+13x } & = & -5 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &27x & = &-15\\\Leftrightarrow & \color{red}{27}x & = &-15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &8x & = &19\\\Leftrightarrow & \color{red}{8}x & = &19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-9}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-5x } & = & 9 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+1}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-3x } & = & -6 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)