Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-10}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-8x } & = & 11 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-4x & = &23\\\Leftrightarrow & \color{red}{-4}x & = &23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-12}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12+15x } & = & 8 \color{red}{ -15x }\color{blue}{+12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &23x & = &20\\\Leftrightarrow & \color{red}{23}x & = &20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+2}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+6x } & = & -11 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &19x & = &-13\\\Leftrightarrow & \color{red}{19}x & = &-13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-13}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-5x } & = & -5 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-1}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+5x } & = & 6 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-5}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-5x } & = & 11 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-8}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+15x } & = & 10 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &28x & = &18\\\Leftrightarrow & \color{red}{28}x & = &18\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{18}{28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)