Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-x } & = & -3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-4}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-10x } & = & 8 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-7}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & 6 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-12}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+7x } & = & 14 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &19x & = &26\\\Leftrightarrow & \color{red}{19}x & = &26\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{26}{19} \\\Leftrightarrow & \color{green}{ x = \frac{26}{19} } & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+1}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-7x } & = & -10 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-x } & = & 6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-5}& = & 2 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+12x } & = & 2 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &25x & = &7\\\Leftrightarrow & \color{red}{25}x & = &7\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{7}{25} \\\Leftrightarrow & \color{green}{ x = \frac{7}{25} } & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)