Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &x & = &28\\\Leftrightarrow & \color{red}{}x & = &28\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 28 \\\Leftrightarrow & \color{green}{ x = 28 } & & \\ & V = \left\{ 28 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+3}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-3x } & = & -6 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+7}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-13x } & = & 4 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-18x & = &-3\\\Leftrightarrow & \color{red}{-18}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-3}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+1}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1-7x } & = & -5 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & 8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & -14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-x } & = & -10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &7x & = &-25\\\Leftrightarrow & \color{red}{7}x & = &-25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+11}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+2x } & = & 5 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)