Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+1}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1+7x } & = & 9 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-15x & = &22\\\Leftrightarrow & \color{red}{-15}x & = &22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-14}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-3x } & = & 6 \color{red}{ +3x }\color{blue}{+14-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &4x & = &20\\\Leftrightarrow & \color{red}{4}x & = &20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{20}{4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & -15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-2}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2+13x } & = & 8 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-14}& = & 14 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-6x } & = & 14 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &x & = &28\\\Leftrightarrow & \color{red}{}x & = &28\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 28 \\\Leftrightarrow & \color{green}{ x = 28 } & & \\ & V = \left\{ 28 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-14}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+4x } & = & 2 \color{red}{ -4x }\color{blue}{+14+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+13}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-13x } & = & -1 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-14\\\Leftrightarrow & \color{red}{-17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)