Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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