Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-x } & = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-15}& = & -7 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15+5x } & = & -7 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & -8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+2}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-11x } & = & 2 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &-21x & = &0\\\Leftrightarrow & \color{red}{-21}x & = &0\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{0}{-21} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-15}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-3x } & = & 3 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+12}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-11x } & = & -11 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-6}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-9x } & = & -14 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-4}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x } & = & 4 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+3}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-11x } & = & -2 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & -13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-21\\\Leftrightarrow & \color{red}{-15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)