Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-1}& = & 10 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+5x } & = & 10 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+12}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+11x } & = & 11 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-6}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-8x } & = & 15 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-2}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-9x } & = & -12 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-20x & = &-10\\\Leftrightarrow & \color{red}{-20}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &12x & = &10\\\Leftrightarrow & \color{red}{12}x & = &10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+5}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+13x } & = & 12 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &20x & = &7\\\Leftrightarrow & \color{red}{20}x & = &7\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{7}{20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{20} } & & \\ & V = \left\{ \frac{7}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-5}& = & -5 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+4x } & = & -5 \color{red}{ -4x }\color{blue}{+5+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-12}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & 9 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-25x & = &21\\\Leftrightarrow & \color{red}{-25}x & = &21\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{21}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{25} } & & \\ & V = \left\{ \frac{-21}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & 12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)