Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+12}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12-14x } & = & 12 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+9}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-7x } & = & -3 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-12\\\Leftrightarrow & \color{red}{-17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8-x } & = & 13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-2x & = &21\\\Leftrightarrow & \color{red}{-2}x & = &21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+9}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9+2x } & = & 1 \color{red}{ -2x }\color{blue}{-9+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-6}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6+5x } & = & -5 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &-8x & = &18\\\Leftrightarrow & \color{red}{-8}x & = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-4}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+14x } & = & -6 \color{red}{ -14x }\color{blue}{+4+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &29x & = &-2\\\Leftrightarrow & \color{red}{29}x & = &-2\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-2}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{29} } & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+11}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-10x } & = & 2 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-13}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13+13x } & = & -1 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &23x & = &12\\\Leftrightarrow & \color{red}{23}x & = &12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{12}{23} } & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)