Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-11}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-5x } & = & -4 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-11}& = & -5 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+4x } & = & -5 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-8}& = & -1 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-12x } & = & -1 \color{red}{ +12x }\color{blue}{+8-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & 13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-7x & = &28\\\Leftrightarrow & \color{red}{-7}x & = &28\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{28}{-7} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-12}& = & -12 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-8x } & = & -12 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-7}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-13x } & = & -4 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-12}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-7x } & = & -7 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-8}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-9x } & = & 6 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-3}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-6x } & = & 3 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-8}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x } & = & 10 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &23x & = &18\\\Leftrightarrow & \color{red}{23}x & = &18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 5 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-25x & = &11\\\Leftrightarrow & \color{red}{-25}x & = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)