Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+8}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-13x } & = & 2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+10}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+6x } & = & -5 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-14}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-9x } & = & -14 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+5}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5+12x } & = & -5 \color{red}{ -12x }\color{blue}{-5+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+2}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-5x } & = & 11 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+12}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-12x } & = & -5 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & 7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-5x & = &15\\\Leftrightarrow & \color{red}{-5}x & = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & 15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-6}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-11x } & = & 8 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-x } & = & -11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)