Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+8}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-6x } & = & 5 \color{red}{ +6x }\color{blue}{-8-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-12}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-10x } & = & 15 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-23x & = &27\\\Leftrightarrow & \color{red}{-23}x & = &27\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{27}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{23} } & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-9}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-7x } & = & 3 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-x } & = & 10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-25\\\Leftrightarrow & \color{red}{-15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+7}& = & 15 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7+4x } & = & 15 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-7}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+13x } & = & 15 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &21x & = &22\\\Leftrightarrow & \color{red}{21}x & = &22\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{22}{21} \\\Leftrightarrow & \color{green}{ x = \frac{22}{21} } & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5-x } & = & 12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-7}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+11x } & = & 1 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &20x & = &8\\\Leftrightarrow & \color{red}{20}x & = &8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)