Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-14\\\Leftrightarrow & \color{red}{-10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+12}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12+4x } & = & -12 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &13x & = &-24\\\Leftrightarrow & \color{red}{13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+4}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-8x } & = & 13 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-x & = &9\\\Leftrightarrow & \color{red}{-}x & = &9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{9}{-1} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+15}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+2x } & = & -3 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &17x & = &-18\\\Leftrightarrow & \color{red}{17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+10}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+5x } & = & -4 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+14}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-5x } & = & 1 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-12}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-5x } & = & 14 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-19x & = &26\\\Leftrightarrow & \color{red}{-19}x & = &26\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{26}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{19} } & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &2x & = &-14\\\Leftrightarrow & \color{red}{2}x & = &-14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-14}{2} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-x } & = & 1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+9}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-11x } & = & 9 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)