Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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