Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & 14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & 1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-13}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-11x } & = & -12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-21x & = &1\\\Leftrightarrow & \color{red}{-21}x & = &1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+15}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-5x } & = & -14 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &7x & = &-29\\\Leftrightarrow & \color{red}{7}x & = &-29\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-29}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{7} } & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-5}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-4x } & = & 13 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & -14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-26\\\Leftrightarrow & \color{red}{-10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-4}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-3x } & = & -10 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-13}& = & -11 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+10x } & = & -11 \color{red}{ -10x }\color{blue}{+13+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &21x & = &2\\\Leftrightarrow & \color{red}{21}x & = &2\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{2}{21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{21} } & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &x & = &21\\\Leftrightarrow & \color{red}{}x & = &21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 21 \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+5}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-5x } & = & -9 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)