Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-5}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-10x } & = & -13 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+2}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-9x } & = & 7 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-3}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-5x } & = & -11 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+13}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13-4x } & = & 15 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+4}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-5x } & = & 8 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-9}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-5x } & = & 13 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-14}& = & 14 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-6x } & = & 14 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-17x & = &28\\\Leftrightarrow & \color{red}{-17}x & = &28\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{28}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{17} } & & \\ & V = \left\{ \frac{-28}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+8}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8-11x } & = & 12 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+1}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-6x } & = & 1 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)