Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+14}& = & 9 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+4x } & = & 9 \color{red}{ -4x }\color{blue}{-14+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+5}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-5x } & = & -3 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-10}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & 3 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-25x & = &13\\\Leftrightarrow & \color{red}{-25}x & = &13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{25} } & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & -9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-20\\\Leftrightarrow & \color{red}{-10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-20}{-10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x } & = & -7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+5}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-8x } & = & -10 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-8}& = & 1 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-15x } & = & 1 \color{red}{ +15x }\color{blue}{+8-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)