Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+5}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-13x } & = & -9 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-6}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & 14 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-9}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+14x } & = & 12 \color{red}{ -14x }\color{blue}{+9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &29x & = &21\\\Leftrightarrow & \color{red}{29}x & = &21\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{21}{29} \\\Leftrightarrow & \color{green}{ x = \frac{21}{29} } & & \\ & V = \left\{ \frac{21}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+15}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+3x } & = & -7 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-13}& = & 6 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13+9x } & = & 6 \color{red}{ -9x }\color{blue}{+13+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &16x & = &19\\\Leftrightarrow & \color{red}{16}x & = &19\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{19}{16} \\\Leftrightarrow & \color{green}{ x = \frac{19}{16} } & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-x } & = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &6x & = &21\\\Leftrightarrow & \color{red}{6}x & = &21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & 7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-9}& = & -4 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-6x } & = & -4 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)