Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+11}& = & -14 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+3x } & = & -14 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &16x & = &-25\\\Leftrightarrow & \color{red}{16}x & = &-25\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-25}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{16} } & & \\ & V = \left\{ \frac{-25}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-12}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-13x } & = & -14 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-3}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-13x } & = & -12 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-28x & = &-9\\\Leftrightarrow & \color{red}{-28}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{28} } & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & 1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+11}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & 7 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+3}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3+11x } & = & -3 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &23x & = &-6\\\Leftrightarrow & \color{red}{23}x & = &-6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{23} } & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-14}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-4x } & = & 9 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &7x & = &23\\\Leftrightarrow & \color{red}{7}x & = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)