Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-8}& = & 8 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+4x } & = & 8 \color{red}{ -4x }\color{blue}{+8+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+12}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+13x } & = & 5 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &22x & = &-7\\\Leftrightarrow & \color{red}{22}x & = &-7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{22} } & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &14x & = &21\\\Leftrightarrow & \color{red}{14}x & = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+2}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-13x } & = & 10 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+12}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12-11x } & = & 2 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+5}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-7x } & = & 14 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-8}& = & -11 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+2x } & = & -11 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+14}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-3x } & = & 9 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+3}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3+2x } & = & -7 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)