Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+4}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-11x } & = & 1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & -13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & -1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & -5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &x & = &-16\\\Leftrightarrow & \color{red}{}x & = &-16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -16 \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-x } & = & 4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-10}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-11x } & = & -10 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-24x & = &0\\\Leftrightarrow & \color{red}{-24}x & = &0\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{0}{-24} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+5}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5-11x } & = & 4 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-9}& = & 4 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9-10x } & = & 4 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+13}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+15x } & = & -1 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &19x & = &-14\\\Leftrightarrow & \color{red}{19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)