Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+7}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-9x } & = & -3 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-1}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+5x } & = & 6 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+1}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-6x } & = & 12 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-17x & = &11\\\Leftrightarrow & \color{red}{-17}x & = &11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+8}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-4x } & = & 7 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+13}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-9x } & = & 13 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-5}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+13x } & = & -8 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &22x & = &-3\\\Leftrightarrow & \color{red}{22}x & = &-3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{22} } & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+5}& = & 6 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+3x } & = & 6 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &16x & = &1\\\Leftrightarrow & \color{red}{16}x & = &1\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{1}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-8}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-9x } & = & -7 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)